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 y = 0

x − 2(0) = 3

x  = 3

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

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

x − 2y = 3

Putting y = 1

x − 2(1) = 3

x − 2 = 3

x = 3 + 2

x = 5

So x = 5 and y = 1 is a solution.

i.e., (5, 1) is a solution

Putting y = −2

x − 2(−2) = 3

x + 4 = 3

x = 3 − 4

x = −1

So x = −1 and y = −2 is a solution.

i.e., (−1, −2) is a solution

x	3	5	−1
y	0	1	−2

For Equation (2)

3x − 8y = 7

Putting y = 1

3x − 8(1) = 7

3x − 8 = 7

3x = 7 + 8

3x = 15

x = 5

So, x = 5, y = 1 is a solution

i.e., (5, 1) is a solution

3x − 8y = 7

Putting y = −2

3x − 8(−2) = 7

3x + 16 = 7

3x = 7 − 16

3x = −9

x = −3

So, x = −3, y = −2 is a solution

i.e., (−3, −2) is a solution

Putting y = 0

3x − 8(0) = 7

3x + 0 = 7

3x = 7

x = `7/3`

x = 2.3

So, x = 2.3, y = 0 is a solution

i.e., (2.3, 0) is a solution

x	5	−3	2.3
y	1	−2	0

We will plot both equations on the graph,

Since lines intersect at (5, 1)

∴ x = 5, y = 1 is the solution of the pair of equations.