Question

Solve the following system of linear equations graphically:

x + 2y = 3, 2x − 3y + 8 = 0

Answer 1

Our equations are

x + 2y = 3  ....(1)

2x − 3y = −8  ...(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.

x + 2y = 3

x	0	3
y	1.5	0

For Equation (2)

2x − 3y = −8

Putting x = 0

2(0) − 3y = −8

−3y = −8

Y = `(−8)/(−3)`

y = 2.67

So, x = 0, y = 2.67 is a solution

i.e. (0, 2.67) is a solution

2x − 3y = 8

Putting y = 0

2x − 3(0) = −8

2x = −8

x = `(−8)/2`

x = −4

So, x = −4, y = 0 is a solution

i.e., (−4, 0) is a solution

x	0	−4
y	2.67	0

we will plot both equations on the graph

Since lines intersect at (−1, 2)

∴ x = −1, y = 2 is the solution of the pair of equations.