Question #b9b6d

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Question #b9b6d

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Answer 1 · 2017-09-01T20:35:11

The equation of the line in function form is:

$y = 2 x - 7$ $y=2x-7$

Explanation:

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

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

We will use linear combination to solve this.

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

$2 x + 2 y = 10$ $2x+2y=10$

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

After adding the equations together, we get:

$5 x = 20$ $5x=20$

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

$x = 4$ $x=4$

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

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

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

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

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

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

We use point slope form:

$(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$ where $(x_{1}, y_{1})$ $(x_1,y_1)$ is a point on the line, and $m$ $m$ is the slope.

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

The equation of our line is:

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

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