Question

Solve the following system of equations graphically: 

x − 2y = 3, 3x − 8y = 7

Answer 1

Equations are

x − 2y = 3   ...(1)

3x − 8y = 7   ...(2)

For Equation (1)

x − 2y = 3

Putting x = 0

0 − 2y = 3

−2y = 3

y = `-3/2`

y = −1.5

So, x = 0, y = −1.5 is a solution

i.e., (0, −1.5) is a solution

x − 2y = 3

Putting y = 0

x − 2(0) = 3

x − 0 = 3

x = 3

So, x = 3, y = 0 is a solution.

i.e., (3, 0) is a solution

x	0	3
y	−1.5	0

For Equation (2)

3x − 8y = 7

Putting x = 0

3(0) − 8y = 7

− 8y = 7

y = `7/-8`

y = −0.87

So, x = 0, y = −0.87 is a solution

i.e., (0, −0.87) is a solution

3x − 8y = 7

Putting y = 0

3x − 8(0) = 7

3x = 7

x =`7/3`

x = 2.34

So, x = 2.34, y = 0 is a solution

i.e., (2.34, 0) is a solution

x	0	2.34
y	−0.87	0

We will plot both equations on the graph

Since lines intersect at (4, 0.5)

∴ x = 4, y = 0.5 is the solution of the pair of equations.