Question

14. (05.02 LC) What is the value of y in the solution to the following system of equations? (5 points) 2x + y = −4 5x + 3y = −6

Answer 1

`\bf \begin{cases} 2x+y=-4\\ \boxed{y} = -4-2x\\[-0.5em] \hrulefill\\ 5x+3y=-6 \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left(\boxed{-4-2x} \right)}=-6 \\\\\\ 5x-12-6x=-6\implies -x-12 = -6\implies -x=6\implies x = -6 \\\\\\ \stackrel{\textit{since we know that}}{y = -4-2x}\implies y = -4-2(-6)\implies y = -4+12\implies \blacktriangleright y = 8 \blacktriangleleft`