Question

How do you solve `2(x-4) + y=6` and `3x-2(y-3)=13` using substitution?

Answer 1

`(5,4)`

Explanation:

Substitution means rearranging one of the 2 equations in terms of x or y and substituting into the other equation.

Choosing `2(x-4)+y=6` and rearranging to make y the subject.

distribute the bracket.

`2x-8+y=6`

subtract 2x from both sides.

`cancel(2x)cancel(-2x)-8+y=6-2x`

add 8 to both sides.

`cancel(-8)cancel(+8)+y=6+8-2x`

`rArry=14-2xlarrcolor(red)"y is now the subject"`

We can now substitute this into the other equation and solve for x.

`rArr3x-2(color(red)(14-2x)-3)=13`

`rArr3x-2(11-2x)=13`

`rArr3x-22+4x=13`

`rArr7x=35rArrx=35/7=5`

We have `y=14-2x" from above"` and substituting x = 5 will give corresponding value of y.

`x=5rArry=14-(2xx5)=14-10=4`

`"Thus solution is " x=5,y=4`

`color(blue)"As a check"`

`2(5-4)+4=2+4=6color(white)(xx)✔︎`

`"and " (3xx5)-2(4-3)=15-2=13color(white)(xx)✔︎`