Answer:
5 – 6x = 8x + 17
⇔ 5 - 17 = 8x + 6x
⇔ -12 = 14x
⇔ x = -6/7
Step-by-step explanation:
Find the slope of the line passing throught the points (2, 2) and (4, 3).
The formula of a slope:

Substitute:

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:
Substitute:

We have the equation:
<em>cross multiply</em>

<em>add 2 to both sides</em>

<h3>Answer: x = -4.</h3>
Answer:
the system has a unique solution
Step-by-step explanation:
Start with an equation of a line in standard form,

Solve it for y to put it into the slope-intercept form:


The slope is -a/b.
Now look at your system of equations. The slope of the first equation is -a/b = -2/3. The slope of the second equation is -a/b = -6/5.
You have a system of two linear equations with two lines with different slopes, so the lines must intersect at a single point.
Answer: the system has a unique solution