Question

(a) 3x + 7y = 13, 5x + 2y = 12
How do i solve this linear equation using substitution method??

Answer 1

x= 2, y= 1

Explanation:

First label the 2 equations:

3x +7y= 13 -----(1)

5x +2y= 12 -----(2)

Make x or y the subject of formula for one of the equation so that we can substitute its value into the 2nd equation.

Here, I am making y the subject of formula in the 2nd equation.

5x +2y= 12

2y= 12 -5x

`y = 6 - (5)/(2) x` -----(3)

Substitute (3) into (1):

`3x + 7(6 - (5)/(2) x) = 13`

Expand:

`3x + 42 - (35)/(2) x = 13`

Bring constants to one side:

`3x - (35)/(2) x = 13 - 42`

Simplify:

`- (29)/(2) x = - 29`

Multiply by -2 on both sides:

`- 29x = - 58`

Divide by -29 on both sides:

x=2

Substitute x=2 into (1):

3(2) +7y= 13

7y +6= 13

7y= 13 -6 (-6 on both sides)

7y= 7

y= 7 ÷7

y= 1