Question

Question DetailsFind the solution to the system of equations by usingthe substitution method. Please show all of your work.If you do it on paper you can take a picture of it andsubmit that.3y = 6.r – 6 and 6x + 8y = -16Hint: I would solve the first equation for y andsubstitute that into the second equation. Click editbackground and show your work there or take a pictureof the work you did on paper.

Answer 1

We are given the following system of equations

$\begin{gathered} 3y=6x-6\quad eq.1 \\ 6x+8y=-16\quad eq.2 \end{gathered}$

Let us solve this system of equations using the substitution method.

First, we need to solve the eq.1 for y

$\begin{gathered} 3y=6x-6 \\ y=\frac{6x-6}{3} \\ y=\frac{6x}{3}-\frac{6}{3} \\ y=2x-2\quad eq.1 \end{gathered}$

Now substitute the eq.1 into eq.2

$\begin{gathered} 6x+8y=-16\quad eq.2 \\ 6x+8(2x-2)=-16 \\ 6x+16x-16=-16 \\ 22x=-16+16 \\ 22x=0 \\ x=\frac{0}{22} \\ x=0 \end{gathered}$

So, the value of x is 0

Finally, substitute the value of x into eq.1 to get the value of y

$\begin{gathered} y=2x-2\quad eq.1 \\ y=2(0)-2 \\ y=-2 \end{gathered}$

So, the value of y is -2

Therefore, the solution of the system of equations is

$(0,-2)$