Question

Solve using elimination.–10x − 10y = –1010x + 8y = –8

Answer 1

The question asks us to solve the following system of equations by elimination:

`\begin{gathered} -10x-10y=-10 \\ 10x+8y=-8 \end{gathered}`

Solution

`\begin{gathered} -10x-10y=-10\text{ (Equation 1)} \\ 10x+8y=-8\text{ (Equation 2)} \\ \\ \text{Add Equation 1 and 2 together.} \\ \\ -10x-10y+(10x+8y)=-10+(-8) \\ -10x-10y+10x+8y=-10-8 \\ -10x+10x+8y-10y=-18 \\ -2y=-18 \\ \text{Divide both sides by -2} \\ -(2y)/(-2)=-(18)/(-2) \\ \\ \therefore y=9 \\ \\ \text{Substitute the value of y into equation 1.} \\ -10x-10y=-10 \\ -10x-10(9)=-10 \\ -10x-90=-10 \\ Add\text{ 90 to both sides} \\ -10x=-10+90 \\ -10x=80 \\ \text{Divide both sides by -10} \\ -(10x)/(-10)=(80)/(-10) \\ \\ \therefore x=-8 \end{gathered}`

Answer

The solution to the system of equation is:

x = -8

y = 9