Solve by Substitution y=5x-7 and -3x-2y=-12

$y = 5 x - 7$ and $- 3 x - 2 y = - 12$

Step 1

Replace all occurrences of $y$ with $5 x - 7$ in each equation.

Replace all occurrences of $y$ in $- 3 x - 2 y = - 12$ with $5 x - 7$ .

$- 3 x - 2 (5 x - 7) = - 12$

$y = 5 x - 7$

Simplify the left side.

Simplify $- 3 x - 2 (5 x - 7)$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 2 (5 x) - 2 \cdot - 7 = - 12$

$y = 5 x - 7$

Multiply $5$ by $- 2$ .

$- 3 x - 10 x - 2 \cdot - 7 = - 12$

$y = 5 x - 7$

Multiply $- 2$ by $- 7$ .

$- 3 x - 10 x + 14 = - 12$

$y = 5 x - 7$

$- 3 x - 10 x + 14 = - 12$

$y = 5 x - 7$

Subtract $10 x$ from $- 3 x$ .

$- 13 x + 14 = - 12$

$y = 5 x - 7$

$- 13 x + 14 = - 12$

$y = 5 x - 7$

$- 13 x + 14 = - 12$

$y = 5 x - 7$

$- 13 x + 14 = - 12$

$y = 5 x - 7$

Step 2

Solve for $x$ in $- 13 x + 14 = - 12$ .

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

Subtract $14$ from both sides of the equation.

$- 13 x = - 12 - 14$

$y = 5 x - 7$

Subtract $14$ from $- 12$ .

$- 13 x = - 26$

$y = 5 x - 7$

$- 13 x = - 26$

$y = 5 x - 7$

Divide each term in $- 13 x = - 26$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 26$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 26}{- 13}$

$y = 5 x - 7$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 26}{- 13}$

$y = 5 x - 7$

Divide $x$ by $1$ .

$x = \frac{- 26}{- 13}$

$y = 5 x - 7$

$x = \frac{- 26}{- 13}$

$y = 5 x - 7$

$x = \frac{- 26}{- 13}$

$y = 5 x - 7$

Simplify the right side.

Divide $- 26$ by $- 13$ .

$x = 2$

$y = 5 x - 7$

$x = 2$

$y = 5 x - 7$

$x = 2$

$y = 5 x - 7$

$x = 2$

$y = 5 x - 7$

Step 3

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = 5 x - 7$ with $2$ .

$y = 5 (2) - 7$

$x = 2$

Simplify the right side.

Simplify $5 (2) - 7$ .

Multiply $5$ by $2$ .

$y = 10 - 7$

$x = 2$

Subtract $7$ from $10$ .

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

Step 4

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

$(2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 6

Solve by Substitution y=5x-7 and -3x-2y=-12

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