Question

Solve the following pair of simultaneous equations:

$3x+5(y+2)=1$
$3x+8y=0$

• A. $(-8,3)$
• B. $(-4,9)$
• C. $(1,-3)$
• D. $(0,-9)$

Answer 1

The correct option is A $(-8,3)$

The equation $3x+5(y+2)=1$ can be written as $3x+5y+10=1$ or $3x+5y=-9$.Another equation is $3x+8y=0$. Then we get the equations:

$3x+5y=-\mathrm{9.........}\left(1\right)$

$3x+8y=\mathrm{0.........}\left(2\right)$

Subtract Equation 2 from equation 1 to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(3x-3x)+(5y-8y)=-9-0$

i.e. $-3y=-9$

i.e. $y=3$

Substituting this value of $y$ in the equation $3x+8y=0$, we get

$3x+24=0$

i.e. $3x=-24$

i.e. $x=-8$

Hence, the solution of the equations is $x=-8,y=3$.