Question

Solving systems by elimination. -3x + 7y = -16-9x +5y = 16

Answer 1

As given by the question

There are given that the system of the equation:

$\begin{gathered} -3x+7y=-16\ldots(1) \\ -9x+5y=16\ldots(2) \end{gathered}$

Now,

From the equation (1):

$\begin{gathered} -3x+7y=-16 \\ -3x=-16-7y \\ x=\frac{16}{3}+\frac{7}{3}y\ldots(3) \end{gathered}$

Put the value of equation (3) into equation (2)

So,

$\begin{gathered} -9(\frac{16}{3}+\frac{7}{3}y)+5y=16 \\ -3(16+7y)+5y=16 \\ -48-21y+5y=16 \\ -48-16y=16 \\ -16y=64 \\ y=-4 \end{gathered}$

Then,

Put the value of y into the equation (3)

So,

$\begin{gathered} x=\frac{16}{3}+\frac{7}{3}y \\ x=\frac{16}{3}+\frac{7}{3}(-4) \\ x=\frac{16}{3}-\frac{28}{3} \\ x=\frac{16-28}{3} \\ x=-\frac{12}{3} \\ x=-4 \end{gathered}$

Hence, the value of x is -4 and the value of y is -4.