Question

We have two equations
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
In the above equations, what operation should be carried out to make the coefficients of $x$ equal?

• A. Multiply equation (1) by 6 and equation (2) by 4
• B. Multiply equation (1) by 3 and equation (2) by 5
• C. Multiply equation (1) by 5 and equation (2) by 3
• D. Multiply equation (1) by 8 and equation (2) by 3

Answer 1

The correct option is C Multiply equation (1) by 5 and equation (2) by 3

Given that,
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
Coefficient of $x$ in equation (1) is 3.
Coefficient of $x$ in equation (2) is 5.

So, to make $x$ coefficients equal, multiply equation (1) by 5 and equation (2) by 3.

$\text{Equation (1)}\times 5\Rightarrow 15x–20y=5$
$\text{Equation (2)}\times 3\Rightarrow 15x–18y=21$