Question

What is the value of y in the solution to the following system of equations?5x-3y=-112x-6y=-14

Answer 1

Solve for the value of y;

`\begin{gathered} 5x-3y=-11---(1) \\ 2x-6y=-14---(2) \\ \text{Multiply both equations by the coefficients of x} \\ \text{Therefore, multiply (1) by 2 and multiply (2) by 5} \\ 10x-6y=-22---(3) \\ 10x-30y=-70---(4) \\ \text{Subtract (4) from (3)} \\ 24y=48 \\ \text{Divide both sides by 24} \\ y=2 \\ \text{Substitute for the value of y into equation (1)} \\ 5x-3(2)=-11 \\ 5x-6=-11 \\ \text{Add 6 to both sides} \\ 5x-6+6=-11+6 \\ 5x=-5 \\ \text{Divide both sides by 5} \\ x=-1 \end{gathered}`

Therefore, the value of y is 2