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=(16)/(3)+(7)/(3)y\ldots(3) \end{gathered}`

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

So,

`\begin{gathered} -9((16)/(3)+(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=(16)/(3)+(7)/(3)y \\ x=(16)/(3)+(7)/(3)(-4) \\ x=(16)/(3)-(28)/(3) \\ x=(16-28)/(3) \\ x=-(12)/(3) \\ x=-4 \end{gathered}`

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