Question

A system of equations is given below.x + 2y = 24x − 5y = 8Identify the constant that can be multiplied by both sides of the first equation to eliminate the variable x when the equations are added together.thenWrite the revised system of equations.

Answer 1

`constant\rightarrow-4`

Step-by-step explanation: We have to find the constant that when multiplied to the first equation and added to the second, the variable x gets canceled out, the two equations are as follows:

`\begin{gathered} x+2y=2\rightarrow(1) \\ 4x-5y=8\rightarrow(2) \end{gathered}`

Multiplying the equation (1) by -4 and adding it to the equation (2) gives the following answer:

`\begin{gathered} -4*(x+2y)=-4*2\rightarrow-4x-8y=-8 \\ \begin{equation*} -4x-8y=-8 \end{equation*} \\ + \\ \begin{equation*} 4x-5y=8 \end{equation*} \\ ---------------------- \\ -3y=0 \end{gathered}`

Therefore the value of the constant is -4.