Question

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

Answer 1

$y = 1.5x+5\implies y=\cfrac{3}{2}x+5\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y)=2\left( \cfrac{3}{2}x+5 \right)} \\\\\\ 2y=3x+10\implies -3x+2y=10 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{rrrrr} 3x&-&2y&=&7\\ -3x&+&2y&=&10\\\cline{1-5} 0&+&0&=&17 \end{array}\qquad \impliedby \textit{another way of saying \underline{no solutions}}$

well, again, if we were to solve for "y" on each and put them in slope-intercept form, we'd get    $\begin{cases} \cfrac{3}{2}x-\cfrac{7}{2}=y\\\\ y = \cfrac{3}{2}x+5 \end{cases}$

as you can see, they have the same slope, meaning the lines are parallel to each other, however the y-intercept is different, so these are two parallel lines with a gap in between, and parallel lines with a gap never touch each other, thus no intersections and thus no solutions.

Answer 2

Answer:

No solution

Explanation:

3x - 2y = 7

Y=1.5x+5

3x - 2y = 7

-1.5x + y = 5

3x - 2y = 7

2(-1.5x + y = 5)

3x - 2y = 7

-3x + 2y = 10

0 = 17

This is false, which means that there are no solutions.

Hope that helps!