Question

Solve the following pairs of linear equations, graphically :

$2x-3y=-6$ and $x-\frac{y}{2}=1$

• A. $(3,2)$
• B. $(3,3)$
• C. $(4,4)$
• D. $(3,4)$

Answer 1

Answer: (D)

$(3,4)$

Given,
$2x-3y=-6$
$\Rightarrow y=\frac{2x}{3}+2$
Substituting different values of $x$ to get corresponding values of $y$, we get
$(0,2),(3,4),(6,6),(-3,0)$
Plotting these points on the graph, we get the graph of the equation, $2x-3y=-6$
Similarly, given second equation,
$x-\frac{y}{2}=1$
$\Rightarrow y=2(x-1)$
Substituting different values of $x$ to get corresponding values of $y$, we get
$(1,0),(0,-2),(2,2),(-1,-4),(3,4)$
Plotting these points on the graph, we get the graph of the equation, $y=2(x-1)$.
The point of intersection of the graphs of the lines is the solution of the equations which is $(3,4)$.