Algebra Examples

$4 x + 3 y = 8$ and $x - 2 y = - 13$

Step 1

Add $2 y$ to both sides of the equation.

$x = - 13 + 2 y$

$4 x + 3 y = 8$

Step 2

Replace all occurrences of $x$ with $- 13 + 2 y$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $4 x + 3 y = 8$ with $- 13 + 2 y$ .

$4 (- 13 + 2 y) + 3 y = 8$

$x = - 13 + 2 y$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $4 (- 13 + 2 y) + 3 y$ .

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.

$4 \cdot - 13 + 4 (2 y) + 3 y = 8$

$x = - 13 + 2 y$

Step 2.2.1.1.2

Multiply $4$ by $- 13$ .

$- 52 + 4 (2 y) + 3 y = 8$

$x = - 13 + 2 y$

Step 2.2.1.1.3

Multiply $2$ by $4$ .

$- 52 + 8 y + 3 y = 8$

$x = - 13 + 2 y$

$- 52 + 8 y + 3 y = 8$

$x = - 13 + 2 y$

Step 2.2.1.2

Add $8 y$ and $3 y$ .

$- 52 + 11 y = 8$

$x = - 13 + 2 y$

$- 52 + 11 y = 8$

$x = - 13 + 2 y$

$- 52 + 11 y = 8$

$x = - 13 + 2 y$

$- 52 + 11 y = 8$

$x = - 13 + 2 y$

Step 3

Solve for $y$ in $- 52 + 11 y = 8$ .

Tap for more steps...

Step 3.1

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Add $52$ to both sides of the equation.

$11 y = 8 + 52$

$x = - 13 + 2 y$

Step 3.1.2

Add $8$ and $52$ .

$11 y = 60$

$x = - 13 + 2 y$

$11 y = 60$

$x = - 13 + 2 y$

Step 3.2

Divide each term in $11 y = 60$ by $11$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $11 y = 60$ by $11$ .

$\frac{11 y}{11} = \frac{60}{11}$

$x = - 13 + 2 y$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{11 y}{11} = \frac{60}{11}$

$x = - 13 + 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{60}{11}$

$x = - 13 + 2 y$

$y = \frac{60}{11}$

$x = - 13 + 2 y$

$y = \frac{60}{11}$

$x = - 13 + 2 y$

$y = \frac{60}{11}$

$x = - 13 + 2 y$

$y = \frac{60}{11}$

$x = - 13 + 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{60}{11}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = - 13 + 2 y$ with $\frac{60}{11}$ .

$x = - 13 + 2 (\frac{60}{11})$

$y = \frac{60}{11}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 13 + 2 (\frac{60}{11})$ .

Tap for more steps...

Step 4.2.1.1

Multiply $2 (\frac{60}{11})$ .

Tap for more steps...

Step 4.2.1.1.1

Combine $2$ and $\frac{60}{11}$ .

$x = - 13 + \frac{2 \cdot 60}{11}$

$y = \frac{60}{11}$

Step 4.2.1.1.2

Multiply $2$ by $60$ .

$x = - 13 + \frac{120}{11}$

$y = \frac{60}{11}$

$x = - 13 + \frac{120}{11}$

$y = \frac{60}{11}$

Step 4.2.1.2

To write $- 13$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = - 13 \cdot \frac{11}{11} + \frac{120}{11}$

$y = \frac{60}{11}$

Step 4.2.1.3

Combine $- 13$ and $\frac{11}{11}$ .

$x = \frac{- 13 \cdot 11}{11} + \frac{120}{11}$

$y = \frac{60}{11}$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{- 13 \cdot 11 + 120}{11}$

$y = \frac{60}{11}$

Step 4.2.1.5

Simplify the numerator.

Tap for more steps...

Step 4.2.1.5.1

Multiply $- 13$ by $11$ .

$x = \frac{- 143 + 120}{11}$

$y = \frac{60}{11}$

Step 4.2.1.5.2

Add $- 143$ and $120$ .

$x = \frac{- 23}{11}$

$y = \frac{60}{11}$

$x = \frac{- 23}{11}$

$y = \frac{60}{11}$

Step 4.2.1.6

Move the negative in front of the fraction.

$x = - \frac{23}{11}$

$y = \frac{60}{11}$

$x = - \frac{23}{11}$

$y = \frac{60}{11}$

$x = - \frac{23}{11}$

$y = \frac{60}{11}$

$x = - \frac{23}{11}$

$y = \frac{60}{11}$

Step 5

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

$(- \frac{23}{11}, \frac{60}{11})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{23}{11}, \frac{60}{11})$

Equation Form:

$x = - \frac{23}{11}, y = \frac{60}{11}$

Step 7