Question

Solve the following pair of simultaneous equations:

$8a-7b=1$

$4a=3b+5$

• A. $a=8,b=9$
• B. $a=3,b=-8$
• C. $a=7,b=-6$
• D. $a=1,b=-1$

Answer 1

The correct option is A $a=8,b=9$

Multiply the equation $4a=3b+5$ or $4a-3b=5$ by $2$ to make the coefficients of $a$ equal. Then we get the equations:

$8a-7b=\mathrm{1.........}\left(1\right)$

$8a-6b=\mathrm{10.........}\left(2\right)$

Subtract Equation (2) from Equation (1) to eliminate $a$, because the coefficients of $a$ are the same. So, we get

$(8a-8a)+(-7b+6b)=1-10$

i.e. $-b=-9$

i.e. $b=9$

Substituting this value of $b$ in the equation $8a-7b=1$, we get

$8a-63=1$

i.e. $8a=64$

i.e. $a=8$

Hence, the solution of the equations is $a=8,b=9$.