Question

How do you solve by substitution `1/2x+2y=12` and `x-2y=6`?

Answer 1

`x=12,y=3`

Explanation:

Plugging the second equation

`x=6+2y` in the first one we get

`1/2*(6+2y)+2y=12`

`1/2*6+1/2*2y+2y=12`
simplifying we get

`3+y+2y=12`

`3+3y=12`
so

`3y=9`

`y=3`

so `x=6+2*3=6+6=12`

Answer 2

`x=12, \ y=3`

Explanation:

The given linear equations

`1/2x+2y=12\ ..........(1)`

`x-2y=6\ ..........(2)`

substituting the value of `x=6+2y` from (2) in (1) as follows

`1/2(6+2y)+2y=12`

`3+y+2y=12`

`3y=9`

`y=3`

substituting `y=3` in (1) we get

`1/2x+2(3)=12`

`1/2x+6=12`

`1/2x=6`

`x=12`

Answer 3

The solution is the point `(12,3)`.

Explanation:

Solve system of equations:

Equation 1: `1/2x+2y=12`

Equation 2: `x-2y=6`

Solve Equation 1 for `x`.

`1/2x+2y=12`

Multiply both sides by `2`.

`x+4y=24`

Subtract `4y` from both sides.

`x=24-4y`

Substitute `24-4y` for `x` in Equation 2 and solve for `y`.

`x-2y=6`

`24-4y-2y=6`

Simplify.

`24-6y=6`

Subtract `24` from both sides.

`-6y=6-24`

Simplify.

`-6y=-18`

Divide both sides by `-6`.

`y=(-18)/(-6)`

`y=3`

Substitute `3` for `y` in Equation 1.

`1/2x+2y=12`

`1/2x+2(3)=12`

`1/2x+6=12`

Subtract `6` from both sides.

`1/2x=12-6`

Simplify.

`1/2x=6`

Multiply both sides by `2`.

`x=12`

The solution is the point `(12,3)`.

graph{(1/2x+2y-12)(x-2y-6)=0 [3.5, 23.5, -3.2, 6.8]}