Question

$$\begin{gathered} 4x+3y=5, \\ 2y-x=7. \end{gathered}$$

Answer 1

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively.
Graph of 4x + 3y = 5

4x + 3y = 5
⇒ 3y = (5 − 4x)
∴ $y=\frac{5-4x}{3}$ .............(i)
Putting x = −1, we get y = 3.
Putting x = 2, we get y = −1.
Putting x = 5, we get y = −5.
Thus, we have the following table for the equation 4x + 3y = 5.

x	−1	2	5
y	3	−1	−5

Now, plot the points A(−1 , 3) , B(2 , −1) and C(5, −5) on the graph paper.
Join AB and BC to get the graph line AC. Extend it on both ways.
Thus, AC is the graph of 4x + 3y = 5.

Graph of 2y − x = 7
2y − x = 7
⇒ 2y = (7 + x)
∴ $y=\frac{7+x}{2}$.............(ii)
Putting x = −1, we get y = 3.
Putting x = 3, we get y = 5.
Putting x = −3, we get y = 2.
Thus, we have the following table for the equation 2y − x = 7.

x	−1	3	−3
y	3	5	2

Now, plot the points P(3, 5), Q(−3, 2). The point A(−1, 3) has already been plotted. Join PA and QA and extend it on both ways.
Thus, PQ is the graph of 2y − x = 7.

The two graph lines intersect at A(−1 , 3).
∴ The solution of the given system of equations is x = −1 and y = 3.