Question

Which graph represents the solution to the following system of equations?A. Graph DB. Graph BC. Graph CD. Graph A

Answer 1

Given,

The pair of equation is:

`\begin{gathered} -x+2y=-6 \\ 3x+4y=-32 \end{gathered}`

Required:

The graph of the solution of the pair of equation.

Taking the equation first as,

`\begin{gathered} -x+2y=-6 \\ -x=-2y-6 \\ x=6+2y \end{gathered}`

Substituting the value of x in equation second.

`\begin{gathered} 3x+4y=-32 \\ 3(6+2y)+4y=-32 \\ 18+6y+4y=-32 \\ 18+10y=-32 \\ 10y=-32-18 \\ 10y=-50 \\ y=-5 \end{gathered}`

Substituting the value of y in above expression.

`\begin{gathered} x=6+2y \\ x=6+2(-5) \\ x=-4 \end{gathered}`

The solution of the equation is (-4, -5).

The coordinates (-4,-5) is shown by graph B.

Hence, graph B represents the solution to the following system of equations