Question

Solve the following equations by using Cramer’s rule:

5x + 3v = 17; 3x + 7y = 31

Answer 1

The equations are

5x + 3y = 17

3x + 7y = 31

Here Δ = `|(5, 3),(3, 7)|`

= 35 – 9

= 26 ≠ 0

∴ We can apply Cramer’s Rule

Now `Delta_x = |(17, 3),(31, 7)|`

= 119 – 93

= 26

`Delta_y = |(5, 17),(3, 31)|`

= 155 – 51

= 104

∴ By Cramer's rule

x = `Delta_x/Delta = 26/26` = 8

y = `Delta_y/Delta = 104/26` = 4

∴ x = 1; y = 4