Question

Solve the following systems of linear equations by using the method of elimination by equating the coefficients:

$3x+2y=11$
$2x+3y=4$
$\left[3\right]$

Answer 1

Solution:
$3x+2y=11$ .....(1)
$2x+3y=4$ .....(2)

Multiply (1) by 2 and (2) by 3. Then, we gets;
$6x+4y=22$ ...(3)
$6x+9y=12$ ...(4)
[1 Mark]

Now using elimination method to solve the given simultaneous equations, subtracting (4) from (3);
$6x+4y=22$
$6x+9y=12$
$\underset{–}{---}$
$-5y=10$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ $y=-2$ [1 Mark]

Putting value of $y$ in (1), we get

$3x+2(-2)=11$
$\Rightarrow$ $3x-4=11$
$\Rightarrow$ $3x=11+4$
$\Rightarrow$ $3x=15$
$\Rightarrow$ $x=5$

Hence, the solution of given simultaneous equations is $x=5$ and $y=-2$. [1 Mark]