Question

Solve each system by elimination. 2x + 4y = -43x + 5y = -3Write the solution as an ordered pair ( , )

Answer 1

The given system of equations is:

`\begin{gathered} 2x+4y=-4\text{ Equation (1)} \\ 3x+5y=-3\text{ Equation (2)} \end{gathered}`

Multiply equation 1 by 3 on both sides, and equation 2 by 3 on both sides:

`\begin{gathered} 3(2x+4y)=3(-4) \\ 6x+12y=-12\text{ Equation (1)} \\ 2(3x+5y)=2(-3) \\ 6x+10y=-6\text{ Equation (2)} \end{gathered}`

Subtract equation (2) from equation (1):

`\begin{gathered} +6x+12y=-12 \\ -6x+10y=-6 \\ ----------- \\ 0+2y=-6 \end{gathered}`

Now, solve for y:

`\begin{gathered} 2y=-6 \\ y=(-6)/(2) \\ y=-3 \end{gathered}`

Replace y in equation (1) and find x:

`\begin{gathered} 2x+4(-3)=-4 \\ 2x-12=-4 \\ 2x=-4+12 \\ 2x=8 \\ x=(8)/(2) \\ x=4 \end{gathered}`

Answer: The solution is (4, -3)