Question

Solve the following simultaneous equations by the substitution method.

3x + 4y = 37, 7x + 9y = 85

Answer 1

Given simultaneous equations:

3x + 4y = 37

7x + 9y = 85

Step 1: Express (x) in terms of (y) from the first equation:

3x + 4y = 37

⇒ 3x = 37 – 4y

⇒ `x = (37 - 4y)/3`

Step 2: Substitute `(x = (37 - 4y)/3)` into the second equation:

7x + 9y = 85 

⇒ `7((37 - 4y)/(3)) + 9y = 85`

Multiply both sides by 3 to clear the denominator:

7(37 – 4y) + 27y = 255

Calculate:

259 – 28y + 27y = 255 

259 – y = 255 

–y = 255 – 259

 –y = –4

y = 4

Step 3: Substitute (y = 4) back into the expression for (x):

`x = (37 - 4 xx 4)/3`

`x = (37 - 16)/3`

`x = 21/3`

x = 7