Question

Solve the following pair of simultaneous equations.

3x + 2.6y = 16 and x + 5.2y = 27

Answer 1

Given equations:

3x + 2.6y = 16    ...(1)

x + 5.2y = 27    ...(2)

Here, multiplying equations (1) and (2) by 10 to remove decimals:

10(3x) + 10(2.6y) = 10(16)

30x + 26y = 160    ...(3)

10(x) + 10(5.2y) = 10(27)

10x + 52y = 270    ...(4)

Also, multiplying equation (4) by 3:

3(10x) + 3(52y) = 3(270)

30x + 156y = 810    ...(5)

Now, subtracting equation (3) from equation (5):

(30x + 156y) − (30x + 26y) = 810 − 160

30x + 156y − 30x − 26y = 650

156y − 26y = 650

130y = 650

y = `650/130`

∴ y = 5

Let’s substitute y = 5 into equation (2):

x + 5.2(5) = 27

x + 26 = 27

x = 27 − 26

∴ x = 1