Question

Solve the following simultaneous equations by the substitution method.

7x – 10y = 11, 3x – 7y = 2

Answer 1

Given the simultaneous equations:

7x – 10y = 11

3x – 7y = 2

Step 1: Express (x) from one equation

From equation (2):

3x – 7y = 2 

⇒ 3x = 2 + 7y

⇒ `x = (2 + 7y)/(3)`

Step 2: Substitute (x) in equation (1)

Substitute `(x = (2 + 7y)/(3))` into equation (1):

`7((2 + 7y)/(3)) - 10y = 11`

Multiply both sides by 3 to clear the denominator:

7(2 + 7y) – 30y = 33

14 + 49y – 30y = 33

14 + 19y = 33

19y = 33 – 14

19y = 19

y = 1

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

`x = (2 + 7 xx 1)/(3)`

`x = (2 + 7)/(3)`

`x = 9/3`

x = 3