Question

Solve the following system of equations by the elimination method:

$$\begin{gathered} 7x-5y=11 \\ 3x+4y=17 \end{gathered}$$

Answer 1

Step(1): Multiply the given equation needed by a suitable number so that the coefficient of one of the variables says (x or y) become equal.

Given equation,

$$\begin{gathered} 7x-5y=11....................................................\left(1\right) \\ 3x+4y=17....................................................\left(2\right) \end{gathered}$$

Multiply equation (1) $\times 3$ and equation (2) $\times 7$

$$\begin{gathered} 21x-15y=33............................................\left(3\right) \\ 21x+28y=119...........................................\left(4\right) \end{gathered}$$

Subtract the equations (3) and (4) to eliminate one variable. The resulting equation is a linear equation in one variable.

$-43y=-86....................................................\left(5\right)$

$$\begin{gathered} \Rightarrow y=\frac{-86}{-43} \\ \Rightarrow y=2 \end{gathered}$$

Step (2): Substitute this value of the variable in either of the original equations, to get the value of the other variable.

$$\begin{gathered} 7x-5y=11 \\ \Rightarrow 7x-(5\times 2)=11 \\ \Rightarrow 7x-10=11 \\ \Rightarrow 7x=11+10 \\ \Rightarrow 7x=21 \\ \Rightarrow x=\frac{21}{7} \\ \Rightarrow x=3 \end{gathered}$$

Hence ,the solition is $x=3\text{and}y=2$