Precalculus Examples

$- 5 x + 2 y = - 4$ , $10 x + 6 y = 3$

Step 1

Solve for $x$ in $- 5 x + 2 y = - 4$ .

Tap for more steps...

Step 1.1

Subtract $2 y$ from both sides of the equation.

$- 5 x = - 4 - 2 y$

$10 x + 6 y = 3$

Step 1.2

Divide each term in $- 5 x = - 4 - 2 y$ by $- 5$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 5 x = - 4 - 2 y$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 4}{- 5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 4}{- 5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

$x = \frac{- 4}{- 5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

$x = \frac{- 4}{- 5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{4}{5} + \frac{- 2 y}{- 5}$

$10 x + 6 y = 3$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 x + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 x + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 x + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 x + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 x + 6 y = 3$

Step 2

Replace all occurrences of $x$ with $\frac{4}{5} + \frac{2 y}{5}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $10 x + 6 y = 3$ with $\frac{4}{5} + \frac{2 y}{5}$ .

$10 (\frac{4}{5} + \frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $10 (\frac{4}{5} + \frac{2 y}{5}) + 6 y$ .

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.

$10 (\frac{4}{5}) + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1.2.1

Factor $5$ out of $10$ .

$5 (2) (\frac{4}{5}) + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.2.2

Cancel the common factor.

$5 \cdot (2 (\frac{4}{5})) + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.2.3

Rewrite the expression.

$2 \cdot 4 + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$2 \cdot 4 + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.3

Multiply $2$ by $4$ .

$8 + 10 (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.4

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1.4.1

Factor $5$ out of $10$ .

$8 + 5 (2) (\frac{2 y}{5}) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.4.2

Cancel the common factor.

$8 + 5 \cdot (2 (\frac{2 y}{5})) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.4.3

Rewrite the expression.

$8 + 2 (2 y) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$8 + 2 (2 y) + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.5

Multiply $2$ by $2$ .

$8 + 4 y + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$8 + 4 y + 6 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.2

Add $4 y$ and $6 y$ .

$8 + 10 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$8 + 10 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$8 + 10 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

$8 + 10 y = 3$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3

Solve for $y$ in $8 + 10 y = 3$ .

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

Subtract $8$ from both sides of the equation.

$10 y = 3 - 8$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.1.2

Subtract $8$ from $3$ .

$10 y = - 5$

$x = \frac{4}{5} + \frac{2 y}{5}$

$10 y = - 5$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2

Divide each term in $10 y = - 5$ by $10$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $10 y = - 5$ by $10$ .

$\frac{10 y}{10} = \frac{- 5}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 5}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = \frac{- 5}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = \frac{- 5}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Cancel the common factor of $- 5$ and $10$ .

Tap for more steps...

Step 3.2.3.1.1

Factor $5$ out of $- 5$ .

$y = \frac{5 (- 1)}{10}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.2.3.1.2.1

Factor $5$ out of $10$ .

$y = \frac{5 \cdot - 1}{5 \cdot 2}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.3.1.2.2

Cancel the common factor.

$y = \frac{5 \cdot - 1}{5 \cdot 2}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.3.1.2.3

Rewrite the expression.

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

$x = \frac{4}{5} + \frac{2 y}{5}$

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

$x = \frac{4}{5} + \frac{2 y}{5}$

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

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2.3.2

Move the negative in front of the fraction.

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

$x = \frac{4}{5} + \frac{2 y}{5}$

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

$x = \frac{4}{5} + \frac{2 y}{5}$

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

$x = \frac{4}{5} + \frac{2 y}{5}$

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

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 4

Replace all occurrences of $y$ with $- \frac{1}{2}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = \frac{4}{5} + \frac{2 y}{5}$ with $- \frac{1}{2}$ .

$x = \frac{4}{5} + \frac{2 (- \frac{1}{2})}{5}$

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

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{4}{5} + \frac{2 (- \frac{1}{2})}{5}$ .

Tap for more steps...

Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{4 + 2 (- \frac{1}{2})}{5}$

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

Step 4.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = \frac{4 + 2 (\frac{- 1}{2})}{5}$

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

Step 4.2.1.2.2

Cancel the common factor.

$x = \frac{4 + 2 (\frac{- 1}{2})}{5}$

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

Step 4.2.1.2.3

Rewrite the expression.

$x = \frac{4 - 1}{5}$

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

$x = \frac{4 - 1}{5}$

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

Step 4.2.1.3

Subtract $1$ from $4$ .

$x = \frac{3}{5}$

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

$x = \frac{3}{5}$

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

$x = \frac{3}{5}$

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

$x = \frac{3}{5}$

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

Step 5

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

$(\frac{3}{5}, - \frac{1}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{5}, - \frac{1}{2})$

Equation Form:

$x = \frac{3}{5}, y = - \frac{1}{2}$

Step 7