Question

Solve the following pair of linear equations by the substitution method:

$x+2y=-1,2x-3y=12$

Answer 1

Step 1: Given linear equations and Apply the substitution method

$\begin{array}{rcl}x+2y& =& -1....\left(1\right)\\ 2x-3y& =& 12.....\left(2\right)\end{array}$

Write $x$ in terms of $y$ in $\left(1\right)$.

$\begin{array}{rcl}x+2y& =& -1\\ x& =& -1-2y\end{array}$

Substitute the value of $x$ in $\left(2\right)$ to find $y$ as:

$\begin{array}{rcl}2\left(-1-2y\right)-3y& =& 12\\ -2-4y-3y& =& 12\\ -2-7y& =& 12\\ -7y& =& 14\\ y& =& -2\end{array}$

Substitute back $y=-2$ to get $x$:

$\begin{array}{rcl}x& =& -1-2(-2)\\ x& =& -1+4\\ x& =& 3\end{array}$

Hence, the required solution is $x=3\text{and}y=-2$.