Question

How do you write the the ordered pair that is the solution to the following system of equations: `-3x + y = 4` and `-7x + y = 12?`

Answer 1

Solve for one variable and substitute

Explanation:

Subtract the two equations from each other to eliminate the 'y' variable.
`(-3x+y=4)` `-`
`color(white)(..........................)` `larr` Subtracting a (-) by a (-) gives a (+).
`(-7x+y=12)`

`4x = -8`

`x =-2`

Plug in `-2` into one of the two equations to solve for `y`.

`-3(-2)+y=4`

`y=-2`

The solution is `(-2,-2)`

Answer 2

The point of intersection is `(-2,-2)`.

Explanation:

Given:

Equation 1: `-3x+y=4`

Equation 1: `-7x+y=12`

I will use substitution to solve this system of equations. The ordered pair that is the solution is the point at which the two lines intersect.

Solve Equation 1 for `y`.

`-3x+y=4`

Add `3x` to both sides and simplify.

`y=3x+4`

Substitute `3x+4` for `y` in Equation 2 an d solve for `x`.

`-7x+y=12`

`-7x+3x+4=12`

Simplify.

`-4x+4=12`

Subtract `4` from both sides.

`-4x=12-4`

Simplify.

`-4x=8`

Divide both sides by `-4`.

`x=8/(-4)`

Simplify.

`x=-2`

Substitute `-2` for `x` in Equation 1 and solve for `y`.

`-3x+y=4`

`-3(-2)+y=4` `larr` Two negatives make a positive.

Simplify.

`6+y=4`

Subtract `6` from both sides.

`y=4-6`

`y=-2`

Point of Intersection: `(-2,-2)`

graph{(y-3x-4)(y-7x-12)=0 [-11.25, 11.25, -5.625, 5.625]}