Algebra Examples

4 x + 4 y = 1

$4 x + 4 y = 1$ ,

6 x - y = 1

$6 x - y = 1$

Step 1

Solve for

x

$x$ in

4 x + 4 y = 1

$4 x + 4 y = 1$ .

Tap for more steps...

Step 1.1

Subtract

4 y

$4 y$ from both sides of the equation.

4 x = 1 - 4 y

$4 x = 1 - 4 y$

6 x - y = 1

$6 x - y = 1$

Step 1.2

Divide each term in

4 x = 1 - 4 y

$4 x = 1 - 4 y$ by

4

$4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in

4 x = 1 - 4 y

$4 x = 1 - 4 y$ by

4

$4$ .

\frac{4 x}{4} = \frac{1}{4} + \frac{- 4 y}{4}

$\frac{4 x}{4} = \frac{1}{4} + \frac{- 4 y}{4}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of

4

$4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

\frac{4 x}{4} = \frac{1}{4} + \frac{- 4 y}{4}

$\frac{4 x}{4} = \frac{1}{4} + \frac{- 4 y}{4}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{1}{4} + \frac{- 4 y}{4}

$x = \frac{1}{4} + \frac{- 4 y}{4}$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} + \frac{- 4 y}{4}

$x = \frac{1}{4} + \frac{- 4 y}{4}$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} + \frac{- 4 y}{4}

$x = \frac{1}{4} + \frac{- 4 y}{4}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Cancel the common factor of

- 4

$- 4$ and

4

$4$ .

Tap for more steps...

Step 1.2.3.1.1

Factor

4

$4$ out of

- 4 y

$- 4 y$ .

x = \frac{1}{4} + \frac{4 (- y)}{4}

$x = \frac{1}{4} + \frac{4 (- y)}{4}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.1

Factor

4

$4$ out of

4

$4$ .

x = \frac{1}{4} + \frac{4 (- y)}{4 (1)}

$x = \frac{1}{4} + \frac{4 (- y)}{4 (1)}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.3.1.2.2

Cancel the common factor.

x = \frac{1}{4} + \frac{4 (- y)}{4 \cdot 1}

$x = \frac{1}{4} + \frac{4 (- y)}{4 \cdot 1}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.3.1.2.3

Rewrite the expression.

x = \frac{1}{4} + \frac{- y}{1}

$x = \frac{1}{4} + \frac{- y}{1}$

6 x - y = 1

$6 x - y = 1$

Step 1.2.3.1.2.4

Divide

- y

$- y$ by

1

$1$ .

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

6 x - y = 1

$6 x - y = 1$

Step 2

Replace all occurrences of

x

$x$ with

\frac{1}{4} - y

$\frac{1}{4} - y$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of

x

$x$ in

6 x - y = 1

$6 x - y = 1$ with

\frac{1}{4} - y

$\frac{1}{4} - y$ .

6 (\frac{1}{4} - y) - y = 1

$6 (\frac{1}{4} - y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify

6 (\frac{1}{4} - y) - y

$6 (\frac{1}{4} - y) - y$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

6 (\frac{1}{4}) + 6 (- y) - y = 1

$6 (\frac{1}{4}) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.2

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Factor

2

$2$ out of

6

$6$ .

2 (3) (\frac{1}{4}) + 6 (- y) - y = 1

$2 (3) (\frac{1}{4}) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.2.2

Factor

2

$2$ out of

4

$4$ .

2 \cdot (3 (\frac{1}{2 \cdot 2})) + 6 (- y) - y = 1

$2 \cdot (3 (\frac{1}{2 \cdot 2})) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.2.3

Cancel the common factor.

2 \cdot (3 (\frac{1}{2 \cdot 2})) + 6 (- y) - y = 1

$2 \cdot (3 (\frac{1}{2 \cdot 2})) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.2.4

Rewrite the expression.

3 (\frac{1}{2}) + 6 (- y) - y = 1

$3 (\frac{1}{2}) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

3 (\frac{1}{2}) + 6 (- y) - y = 1

$3 (\frac{1}{2}) + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.3

Combine

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

\frac{3}{2} + 6 (- y) - y = 1

$\frac{3}{2} + 6 (- y) - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.1.4

Multiply

- 1

$- 1$ by

6

$6$ .

\frac{3}{2} - 6 y - y = 1

$\frac{3}{2} - 6 y - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

\frac{3}{2} - 6 y - y = 1

$\frac{3}{2} - 6 y - y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 2.2.1.2

Subtract

y

$y$ from

- 6 y

$- 6 y$ .

\frac{3}{2} - 7 y = 1

$\frac{3}{2} - 7 y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

\frac{3}{2} - 7 y = 1

$\frac{3}{2} - 7 y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

\frac{3}{2} - 7 y = 1

$\frac{3}{2} - 7 y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

\frac{3}{2} - 7 y = 1

$\frac{3}{2} - 7 y = 1$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3

Solve for

y

$y$ in

\frac{3}{2} - 7 y = 1

$\frac{3}{2} - 7 y = 1$ .

Tap for more steps...

Step 3.1

Move all terms not containing

y

$y$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract

\frac{3}{2}

$\frac{3}{2}$ from both sides of the equation.

- 7 y = 1 - \frac{3}{2}

$- 7 y = 1 - \frac{3}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.1.2

Write

1

$1$ as a fraction with a common denominator.

- 7 y = \frac{2}{2} - \frac{3}{2}

$- 7 y = \frac{2}{2} - \frac{3}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.1.3

Combine the numerators over the common denominator.

- 7 y = \frac{2 - 3}{2}

$- 7 y = \frac{2 - 3}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.1.4

Subtract

3

$3$ from

2

$2$ .

- 7 y = \frac{- 1}{2}

$- 7 y = \frac{- 1}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.1.5

Move the negative in front of the fraction.

- 7 y = - \frac{1}{2}

$- 7 y = - \frac{1}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

- 7 y = - \frac{1}{2}

$- 7 y = - \frac{1}{2}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2

Divide each term in

- 7 y = - \frac{1}{2}

$- 7 y = - \frac{1}{2}$ by

- 7

$- 7$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in

- 7 y = - \frac{1}{2}

$- 7 y = - \frac{1}{2}$ by

- 7

$- 7$ .

\frac{- 7 y}{- 7} = \frac{- \frac{1}{2}}{- 7}

$\frac{- 7 y}{- 7} = \frac{- \frac{1}{2}}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of

- 7

$- 7$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

\frac{- 7 y}{- 7} = \frac{- \frac{1}{2}}{- 7}

$\frac{- 7 y}{- 7} = \frac{- \frac{1}{2}}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{- \frac{1}{2}}{- 7}

$y = \frac{- \frac{1}{2}}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{- \frac{1}{2}}{- 7}

$y = \frac{- \frac{1}{2}}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{- \frac{1}{2}}{- 7}

$y = \frac{- \frac{1}{2}}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

y = - \frac{1}{2} \cdot \frac{1}{- 7}

$y = - \frac{1}{2} \cdot \frac{1}{- 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3.2

Move the negative in front of the fraction.

y = - \frac{1}{2} \cdot (- \frac{1}{7})

$y = - \frac{1}{2} \cdot (- \frac{1}{7})$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3.3

Multiply

- \frac{1}{2} (- \frac{1}{7})

$- \frac{1}{2} (- \frac{1}{7})$ .

Tap for more steps...

Step 3.2.3.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

y = 1 (\frac{1}{2}) \cdot \frac{1}{7}

$y = 1 (\frac{1}{2}) \cdot \frac{1}{7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3.3.2

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

1

$1$ .

y = \frac{1}{2} \cdot \frac{1}{7}

$y = \frac{1}{2} \cdot \frac{1}{7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3.3.3

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{1}{7}

$\frac{1}{7}$ .

y = \frac{1}{2 \cdot 7}

$y = \frac{1}{2 \cdot 7}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 3.2.3.3.4

Multiply

2

$2$ by

7

$7$ .

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$

Step 4

Replace all occurrences of

y

$y$ with

\frac{1}{14}

$\frac{1}{14}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of

y

$y$ in

x = \frac{1}{4} - y

$x = \frac{1}{4} - y$ with

\frac{1}{14}

$\frac{1}{14}$ .

x = \frac{1}{4} - (\frac{1}{14})

$x = \frac{1}{4} - (\frac{1}{14})$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify

\frac{1}{4} - (\frac{1}{14})

$\frac{1}{4} - (\frac{1}{14})$ .

Tap for more steps...

Step 4.2.1.1

To write

\frac{1}{4}

$\frac{1}{4}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

x = \frac{1}{4} \cdot \frac{7}{7} - \frac{1}{14}

$x = \frac{1}{4} \cdot \frac{7}{7} - \frac{1}{14}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.2

To write

- \frac{1}{14}

$- \frac{1}{14}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

x = \frac{1}{4} \cdot \frac{7}{7} - \frac{1}{14} \cdot \frac{2}{2}

$x = \frac{1}{4} \cdot \frac{7}{7} - \frac{1}{14} \cdot \frac{2}{2}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.3

Write each expression with a common denominator of

28

$28$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 4.2.1.3.1

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{7}{7}

$\frac{7}{7}$ .

x = \frac{7}{4 \cdot 7} - \frac{1}{14} \cdot \frac{2}{2}

$x = \frac{7}{4 \cdot 7} - \frac{1}{14} \cdot \frac{2}{2}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.3.2

Multiply

4

$4$ by

7

$7$ .

x = \frac{7}{28} - \frac{1}{14} \cdot \frac{2}{2}

$x = \frac{7}{28} - \frac{1}{14} \cdot \frac{2}{2}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.3.3

Multiply

\frac{1}{14}

$\frac{1}{14}$ by

\frac{2}{2}

$\frac{2}{2}$ .

x = \frac{7}{28} - \frac{2}{14 \cdot 2}

$x = \frac{7}{28} - \frac{2}{14 \cdot 2}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.3.4

Multiply

14

$14$ by

2

$2$ .

x = \frac{7}{28} - \frac{2}{28}

$x = \frac{7}{28} - \frac{2}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{7}{28} - \frac{2}{28}

$x = \frac{7}{28} - \frac{2}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.4

Combine the numerators over the common denominator.

x = \frac{7 - 2}{28}

$x = \frac{7 - 2}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 4.2.1.5

Subtract

2

$2$ from

7

$7$ .

x = \frac{5}{28}

$x = \frac{5}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{5}{28}

$x = \frac{5}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{5}{28}

$x = \frac{5}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

x = \frac{5}{28}

$x = \frac{5}{28}$

y = \frac{1}{14}

$y = \frac{1}{14}$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

(\frac{5}{28}, \frac{1}{14})

$(\frac{5}{28}, \frac{1}{14})$

Step 6

The result can be shown in multiple forms.

Point Form:

(\frac{5}{28}, \frac{1}{14})

$(\frac{5}{28}, \frac{1}{14})$

Equation Form:

x = \frac{5}{28}, y = \frac{1}{14}

$x = \frac{5}{28}, y = \frac{1}{14}$

Step 7

Enter YOUR Problem