Question

Question #b9b6d

Answer 1

The equation of the line in function form is:

`y=2x-7`

Explanation:

Our first step will be to solve the set of equations:

`3x-2y=10`
`x+y=5`

We will use linear combination to solve this.

We will multiply both sides of the second equation by `2`.

`2x+2y=10`

Then, we will add the equations together. Since `2x+2y` is equal to `10`, we can add `2x+2y` to one side and `10` to the other side and be sure that we are adding the same value to both sides.

After adding the equations together, we get:

`5x=20`

The `y` values cancel out, and we are left with:

`x=4`

Next, we determine the `y` output when `x` equals `4`.

`4color(red)(-4)+y=5color(red)(-4)`
`y=1`

Okay. The solution of the system is `(4,1)`. Now we can move on.

To get our final answer, we will conveniently use point-slope form.

Since the line is parallel to `y=2x+1`, we know that the line must have a slope of `2`, because in function form, the coefficient on x is the line's slope.

We know the slope of the line is `2`, and we know it passes through the point `(4,1)`.

We use point slope form:

`(y-y_1)=m(x-x_1)` where `(x_1,y_1)` is a point on the line, and `m` is the slope.

`(y-color(red)1)=color(red)2(x-color(red)4)`

The equation of our line is:

`y-1=2(x-4)` or `y=2x-7`