Question

Solve the following equations by substitution method.

$2x-3y-3=7;4x-5y-5=10$

• A. $x=\frac{-7}{2},y=-5$
• B. $x=\frac{-3}{2},y=-5$
• C. $x=\frac{-1}{2},y=-5$
• D. $x=\frac{-5}{2},y=-5$

Answer 1

The correct option is D $x=\frac{-5}{2},y=-5$

Rewriting the given equations, we get
$2x-3y=10$ ...(i)
$4x-5y=15$ ...(ii)
We pick either of the equations and write one variable in terms of the other. Consider the Equation (i) and write it as $x=\frac{10+3y}{2}$ ...(iii)
Substitute the value of $x=\frac{10+3y}{2}$ in Equation (ii). we get,
$4\left(\frac{10+3y}{2}\right)-5y=15$
$\Rightarrow 20+6y-5y=15$
$\Rightarrow y=-5$
Substituting this value of $y=-5$ in Equation (iii). we get,
$x=\frac{10+3(-5)}{2}=\frac{-5}{2}$

$\therefore x=\frac{-5}{2},y=-5$