Question

Solve the following system of equations graphically:

$$\begin{gathered} 3x+2y=12 \\ 5x-2y=4 \end{gathered}$$

Answer 1

The given equations are:
$$\begin{gathered} 3x+2y=12.....\left(i\right) \\ 5x-2y=4.....\left(ii\right) \end{gathered}$$
From (i), write y in terms of x
$y=\frac{12-3x}{2}.....\left(iii\right)$
Now, substitute different values of x in (iii) to get different values of y
For x = 0, $y=\frac{12-3x}{2}=\frac{12-0}{2}=6$
For x = 2, $y=\frac{12-3x}{2}=\frac{12-6}{2}=3$
For x = 4, $y=\frac{12-3x}{2}=\frac{12-12}{2}=0$
Thus, the table for the first equation (3x + 2y = 12) is

x	0	2	4
y	6	3	0

Now, plot the points A(0, 6), B(2, 3) and C(4, 0) on a graph paper and join
A, B and C to get the graph of 3x + 2y = 12.
From (ii), write y in terms of x
$y=\frac{5x-4}{2}.....\left(iv\right)$
Now, substitute different values of x in (iv) to get different values of y
For x = 0, $y=\frac{5x-4}{2}=\frac{0-4}{2}=-2$
For x = 2, $y=\frac{5x-4}{2}=\frac{10-4}{2}=3$
For x = 4, $y=\frac{5x-4}{2}=\frac{20-4}{2}=8$
Thus, the table for the first equation (5x − 2y = 4) is

x	0	2	4
y	−2	3	8

Now, plot the points D(0, −2), E(2, 3) and F(4, 8) on the same graph paper and join
D, E and F to get the graph of 5x − 2y = 4.



From the graph it is clear that, the given lines intersect at (2, 3).
Hence, the solution of the given system of equations is (2, 3).