Question

Solve each system of the equation by elimination method. 2x-7y=9x+2y=10

Answer 1

We are given the following two equations

$\begin{gathered} 2x-7y=9\quad eq.1 \\ x+2y=10\quad eq.2 \end{gathered}$

We are asked to solve the system of equations using the elimination method.

First, we need to multiply the eq.2 by 2 then we will subtract the eq.2 from eq.1

$\begin{gathered} 2\times(x+2y=10) \\ 2x+4y=20 \end{gathered}$$\begin{gathered} -11y=-11 \\ \frac{-11y}{-11}=\frac{-11}{-11} \\ y=1 \end{gathered}$

Now substitute this value of y into the other equation to get the value of x.

$\begin{gathered} 2x+4(1)=20 \\ 2x+4=20 \\ 2x=20-4 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}$

Therefore, the solution of the system of equations is

$(8,1)$