Question

Solve the following simultaneous equations by the substitution method.

3x – 2y = 0, 5x + y = 13

Answer 1

Given equations: 3x – 2y = 0, 5x + y = 13

Step 1: Solve one equation for one variable.

From the first equation:

3x – 2y = 0

⇒ 3x = 2y

⇒ `y = (3x)/2`

Step 2: Substitute this expression for (y) into the second equation:

5x + y = 13

⇒ `5x + (3x)/2 = 13`

Multiply both sides by 2 to eliminate the denominator:

`2 xx (5x) + 2 xx (3x)/2 = 2 xx 13`

⇒ 10x + 3x = 26

⇒ 13x = 26

⇒ x = 2

Step 3: Substitute (x = 2) back into `(y = (3x)/(2))`: 

`y = (3 xx 2)/2`

y = 3