Solve by Substitution 5x+y=-3 , 7x-3y=-13

$5 x + y = - 3$ , $7 x - 3 y = - 13$

Step 1

Subtract $5 x$ from both sides of the equation.

$y = - 3 - 5 x$

$7 x - 3 y = - 13$

Step 2

Replace all occurrences of $y$ with $- 3 - 5 x$ in each equation.

Replace all occurrences of $y$ in $7 x - 3 y = - 13$ with $- 3 - 5 x$ .

$7 x - 3 (- 3 - 5 x) = - 13$

$y = - 3 - 5 x$

Simplify the left side.

Simplify $7 x - 3 (- 3 - 5 x)$ .

Simplify each term.

Apply the distributive property.

$7 x - 3 \cdot - 3 - 3 (- 5 x) = - 13$

$y = - 3 - 5 x$

Multiply $- 3$ by $- 3$ .

$7 x + 9 - 3 (- 5 x) = - 13$

$y = - 3 - 5 x$

Multiply $- 5$ by $- 3$ .

$7 x + 9 + 15 x = - 13$

$y = - 3 - 5 x$

$7 x + 9 + 15 x = - 13$

$y = - 3 - 5 x$

Add $7 x$ and $15 x$ .

$22 x + 9 = - 13$

$y = - 3 - 5 x$

$22 x + 9 = - 13$

$y = - 3 - 5 x$

$22 x + 9 = - 13$

$y = - 3 - 5 x$

$22 x + 9 = - 13$

$y = - 3 - 5 x$

Step 3

Solve for $x$ in $22 x + 9 = - 13$ .

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

Subtract $9$ from both sides of the equation.

$22 x = - 13 - 9$

$y = - 3 - 5 x$

Subtract $9$ from $- 13$ .

$22 x = - 22$

$y = - 3 - 5 x$

$22 x = - 22$

$y = - 3 - 5 x$

Divide each term in $22 x = - 22$ by $22$ and simplify.

Divide each term in $22 x = - 22$ by $22$ .

$\frac{22 x}{22} = \frac{- 22}{22}$

$y = - 3 - 5 x$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 x}{22} = \frac{- 22}{22}$

$y = - 3 - 5 x$

Divide $x$ by $1$ .

$x = \frac{- 22}{22}$

$y = - 3 - 5 x$

$x = \frac{- 22}{22}$

$y = - 3 - 5 x$

$x = \frac{- 22}{22}$

$y = - 3 - 5 x$

Simplify the right side.

Divide $- 22$ by $22$ .

$x = - 1$

$y = - 3 - 5 x$

$x = - 1$

$y = - 3 - 5 x$

$x = - 1$

$y = - 3 - 5 x$

$x = - 1$

$y = - 3 - 5 x$

Step 4

Replace all occurrences of $x$ with $- 1$ in each equation.

Replace all occurrences of $x$ in $y = - 3 - 5 x$ with $- 1$ .

$y = - 3 - 5 \cdot - 1$

$x = - 1$

Simplify the right side.

Simplify $- 3 - 5 \cdot - 1$ .

Multiply $- 5$ by $- 1$ .

$y = - 3 + 5$

$x = - 1$

Add $- 3$ and $5$ .

$y = 2$

$x = - 1$

$y = 2$

$x = - 1$

$y = 2$

$x = - 1$

$y = 2$

$x = - 1$

Step 5

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

$(- 1, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 2)$

Equation Form:

$x = - 1, y = 2$

Step 7

Solve by Substitution 5x+y=-3 , 7x-3y=-13

Related Questions

Support LCMGCF.com by disabling your adblocker.