Question

Solve this system using the substitution method 10 = -10x-5y. -7x-14 = 7y What is x+y

Answer 1

Explanation:

We first solve for y in the second equation.

The second equation is

`-7x-14=7y`

dividing both sides by 7 gives

`(-7x-14)/(7)=y`
`-x-2=y`

We now substitute the value of y into the first equation.

The first equation is

`10=-10x-5y`

substituting the value of y gives

`10=-10x-5(-x-2)`

Simplifying the right-hand side gives

`10=-10x+5x+10`
`10=-5x+10`

Subtracting 10 from both sides gives

`\begin{gathered} -5x=0 \\ \boxed{x=0} \end{gathered}`

With the value of x in hand, we now put it into -7x - 14 = 7y to get

`-7(0)-14=7y`
`-14=7y`

Dividing both sides by 7 gives

`\boxed{y=-2.}`

Hence, to conclude, the solution to the system is

x = 0

y = -2.

Therefore, x + y = -2