Question

Solve the following systems of linear equations by using the method of elimination by equating the coefficients:
$8x+5y=9$
$3x+2y=4$

Answer 1

The given system of equation is

$8x+5y=9$ .....(i)

$3x+2y=4$ .....(ii)

Let us eliminate $x$ from the given equations. The coefficients of $x$ in the given equations are $8$ and $3$ respectively. The L.C.M. of $8$ and $3$ is $24$. So, we make both the coefficients equal to $24$.

Multiplying both sides of equation (i) by $3$ and equation (ii) by $8$, we get:

$24x+15y=27$

$24x+16y=32$

Substracting (iv) from (iii), we get:

$-y=-5⟹y=5$

Putting $y=5$ in (i), we get:

$8x+25=9⟹8x=-16$

$⟹x=-2$

Hence, the solution of the given system of equations is $x=-2,y=5$.