Question

Solve the following simultaneous equations by the substitution method.

3x + 4y = 13, 5x + 9y = 24

Answer 1

Given equations:

1. 3x + 4y = 13
2. 5x + 9y = 24

Step 1: Solve equation (1) for (x):

3x + 4y = 13 

⇒ 3x = 13 – 4y

⇒ `x = (13 - 4y)/3`

Step 2: Substitute this value of (x) into equation (2):

`5((13 - 4y)/3) + 9y = 24` 

Multiply both sides by 3 to clear the denominator:

5(13 – 4y) + 27y = 72 

Calculate and simplify:

65 – 20y + 27y = 72

⇒ 65 + 7y = 72

7y = 72 – 65

7y = 7

⇒ y = 1

Step 3: Substitute (y = 1) back into the expression for (x):

`x = (13 - 4(1))/3`

`x = (13 - 4)/3`

`x = 9/3`

x = 3