Solve by Substitution -4x+y=-9 , 5x+2y=3

$- 4 x + y = - 9$ , $5 x + 2 y = 3$

Step 1

Add $4 x$ to both sides of the equation.

$y = - 9 + 4 x$

$5 x + 2 y = 3$

Step 2

Replace all occurrences of $y$ with $- 9 + 4 x$ in each equation.

Replace all occurrences of $y$ in $5 x + 2 y = 3$ with $- 9 + 4 x$ .

$5 x + 2 (- 9 + 4 x) = 3$

$y = - 9 + 4 x$

Simplify the left side.

Simplify $5 x + 2 (- 9 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$5 x + 2 \cdot - 9 + 2 (4 x) = 3$

$y = - 9 + 4 x$

Multiply $2$ by $- 9$ .

$5 x - 18 + 2 (4 x) = 3$

$y = - 9 + 4 x$

Multiply $4$ by $2$ .

$5 x - 18 + 8 x = 3$

$y = - 9 + 4 x$

$5 x - 18 + 8 x = 3$

$y = - 9 + 4 x$

Add $5 x$ and $8 x$ .

$13 x - 18 = 3$

$y = - 9 + 4 x$

$13 x - 18 = 3$

$y = - 9 + 4 x$

$13 x - 18 = 3$

$y = - 9 + 4 x$

$13 x - 18 = 3$

$y = - 9 + 4 x$

Step 3

Solve for $x$ in $13 x - 18 = 3$ .

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

Add $18$ to both sides of the equation.

$13 x = 3 + 18$

$y = - 9 + 4 x$

Add $3$ and $18$ .

$13 x = 21$

$y = - 9 + 4 x$

$13 x = 21$

$y = - 9 + 4 x$

Divide each term in $13 x = 21$ by $13$ and simplify.

Divide each term in $13 x = 21$ by $13$ .

$\frac{13 x}{13} = \frac{21}{13}$

$y = - 9 + 4 x$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{21}{13}$

$y = - 9 + 4 x$

Divide $x$ by $1$ .

$x = \frac{21}{13}$

$y = - 9 + 4 x$

$x = \frac{21}{13}$

$y = - 9 + 4 x$

$x = \frac{21}{13}$

$y = - 9 + 4 x$

$x = \frac{21}{13}$

$y = - 9 + 4 x$

$x = \frac{21}{13}$

$y = - 9 + 4 x$

Step 4

Replace all occurrences of $x$ with $\frac{21}{13}$ in each equation.

Replace all occurrences of $x$ in $y = - 9 + 4 x$ with $\frac{21}{13}$ .

$y = - 9 + 4 (\frac{21}{13})$

$x = \frac{21}{13}$

Simplify the right side.

Simplify $- 9 + 4 (\frac{21}{13})$ .

Multiply $4 (\frac{21}{13})$ .

Combine $4$ and $\frac{21}{13}$ .

$y = - 9 + \frac{4 \cdot 21}{13}$

$x = \frac{21}{13}$

Multiply $4$ by $21$ .

$y = - 9 + \frac{84}{13}$

$x = \frac{21}{13}$

$y = - 9 + \frac{84}{13}$

$x = \frac{21}{13}$

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = - 9 \cdot \frac{13}{13} + \frac{84}{13}$

$x = \frac{21}{13}$

Combine $- 9$ and $\frac{13}{13}$ .

$y = \frac{- 9 \cdot 13}{13} + \frac{84}{13}$

$x = \frac{21}{13}$

Combine the numerators over the common denominator.

$y = \frac{- 9 \cdot 13 + 84}{13}$

$x = \frac{21}{13}$

Simplify the numerator.

Multiply $- 9$ by $13$ .

$y = \frac{- 117 + 84}{13}$

$x = \frac{21}{13}$

Add $- 117$ and $84$ .

$y = \frac{- 33}{13}$

$x = \frac{21}{13}$

$y = \frac{- 33}{13}$

$x = \frac{21}{13}$

Move the negative in front of the fraction.

$y = - \frac{33}{13}$

$x = \frac{21}{13}$

$y = - \frac{33}{13}$

$x = \frac{21}{13}$

$y = - \frac{33}{13}$

$x = \frac{21}{13}$

$y = - \frac{33}{13}$

$x = \frac{21}{13}$

Step 5

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

$(\frac{21}{13}, - \frac{33}{13})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{21}{13}, - \frac{33}{13})$

Equation Form:

$x = \frac{21}{13}, y = - \frac{33}{13}$

Step 7

Solve by Substitution -4x+y=-9 , 5x+2y=3

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