Question

Solve each system by substitution. y=5x-7 -3x-2y=-12 Type in your solution (x,y)

Answer 1

Given system :

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

Solution to the system :

Substitute the given value of y into the equation -3x-2y=-12

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

Distribute -2 through the parentheses

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

Collect like terms

$- 13x + 14 = - 12$

Move the constant to the right-hand side and change its sign

$- 13x = - 12 - 14$

Calculate the sum and divide both sides of equation by -13

$x = 2$

Now, Substitute the given value of x into y=5x-7

$y = 5(2) - 7$

Multiply the numbers

$y = 10 - 7$

Subtract the numbers

$y = 3$

The possible solution of the system is the ordered pair (x,y)

$(x,y)=(2,3)$