Question 55977

Jan 31, 2017

Write both equations in slope-intercept form and it will be easier to tell. Details follow...

Explanation:

Slope-intercept form is $y = m x + b$
Writing these equations in this way, we get

$y = \frac{1}{4} x - \frac{9}{4}$ for the first one (divided every term by 4)

slope = $\frac{1}{4}$, $y$-intercept = $- \frac{9}{4}$

$y = \frac{3}{8} x - \frac{9}{4}$ for the second one (moved the $y$ term and divided each by 8)

slope = $\frac{3}{8}$, $y$-intercept = $- \frac{9}{4}$

Since the two equations have different slopes, they are not parallel. If they were parallel, there would be no intersection of the lines, and hence, no solution.

Also, they are not the same line (because they not not simplify to the same equation. If they did, there would be infinitely many solutions.

So, we realize there is only one solution. Generally, to find it, you set the two right sides equal (since both equal $y$) and solve for $x$.

Here, it is simpler. The $y$-intercept is the same for both lines. so this is the point of intersection - the only solution (x=0, y=-9/4)