Question

5x+y=-10 4x-7y=-8 Substition Method (Show it step by step please!)

Answer 1

x = -2, y = 0

Explanation:

This is a systems of equations. Using substitution, we solve for a single variable, plug it in to solve for the other, and solve that one back in to solve for the original. Let's solve it.

5x + y = -10

Subtract 5x from both sides.

y = -5x - 10

Now that we have y isolated, we can plug it in to the other equation.

4x - 7(-5x-10) = -8

Distribute.

4x + 35x + 70 = -8

Subtract 70 from both sides and simplify.

39x = -78

Divide both sides by 39.

x = -2

Now that we have x as -2, we plug it in to the original.

5(-2) + y = -10

Simplify.

-10 + y = -10

Add 10 to both sides.

y = 0

x = -2, y = 0

Answer 2

`\left\{\begin{array}{ccc}5x+y=-10&|\text{subtract 5x from both sides}\\4x-7y=-8\end{array}\right\\\left\{\begin{array}{ccc}y=-5x-10&|\text{substitute to the second equation}\\4x-7y=-8\end{array}\right\\\\4x-7(-5x-10)=-8\qquad\text{use distributive property}\\\\4x+(-7)(-5x)+(-7)(-10)=-8\\\\4x+35x+70=-8\qquad\text{subtract 70 from both sides}\\\\39x=-78\qquad\text{divide both sides by 39}\\\\\boxed{x=-2}\\\\\text{Put the value of x to the first equation}\\\\y=-5(-2)-10\\\\y=10-10\\\\\boxed{y=0}`

`Answer:\ \boxed{x=-2\ and\ y=0}`