Question

Solve the following equations by the substitution method :

$$\begin{gathered} \frac{x+11}{7}+2y=10 \\ 3x=8+\frac{y+7}{11} \end{gathered}$$

Answer 1

Step(1):Express one variable (say x) in terms of other variable (say y) from one of the given equations.

Given equations,

$$\begin{gathered} \frac{x+11}{7}+2y=10................................................\left(1\right) \\ 3x=8+\frac{y+7}{11}....................................................\left(2\right) \end{gathered}$$

Consider the first equation,

$\frac{x+11}{7}+2y=10$

multiplying the equation throughout by 7

$$\begin{gathered} x+11+14y=70 \\ x=70-11-14y \\ x=59-14y...............................................\left(3\right) \end{gathered}$$

Step (2):Substitute the value of $x=59-14y$ in equation (2) to get a linear equations in y which can be solved.

Consider the second equation,

$3x=8+\frac{y+7}{11}$

multiplying the equation throughout by 11

$$\begin{gathered} 33x=88+y+7 \\ \Rightarrow 33(59-14y)=88+y+7 \\ \Rightarrow 1947-462y=95+y \\ \Rightarrow 1947-95=y+462y \\ \Rightarrow 1852=463y \\ \Rightarrow y=\frac{1852}{463} \\ \Rightarrow y=4 \end{gathered}$$

Step (3) : Substitute the values of $y=4$ obtained from (2) in equation (3), we get the values for x

$$\begin{gathered} x=59-14y \\ \Rightarrow x=59-(14\times 4) \\ \Rightarrow x=59-56 \\ \Rightarrow x=3 \end{gathered}$$

Hence, the values of $x=3andy=4$