Question

The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
–3 5
0 4
Line 2
x y
0 4
6 2


A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many

Answer 1

@jdoe0001 @just_one_last_goodbye @k_lynn @bibby @Bookworm14 @HelpBlahBlahBlah @BassCatcher15 @xapproachesinfinity @xX_GamerGirl_Xx @Squirrels @HelpBlahBlahBlah @Godlovesme @EclipsedStar @EmmaElizabeth @abb0t

Answer 2

well, you could start off by getting their slopes

if their slopes are equal, they're parallel lines, thus they do not intersect, thus no solution

if not, then they do touch, thus 1 solution

Answer 3

So A? @jdoe0001

Answer 4

hmmm well.. what slopes did you get?

Answer 5

for line 1 -3,4

Answer 6

3,4? may want to revise your slopes

Answer 7

\(\large {
\begin{array}{ccllll}
x&y
\\\hline\\
{\color{red}{ -3}}&{\color{blue}{ 5}}\\
{\color{red}{ 0}}&{\color{blue}{ 4}}
\end{array}\qquad
\begin{array}{ccllll}
x&y
\\\hline\\
{\color{red}{ 0}}&{\color{blue}{ 2}}\\
{\color{red}{ 4}}&{\color{blue}{ 6}}
\end{array}\qquad
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
}\)

Answer 8

-3y-0y/0x-4x

Answer 9

or is it -3y-4y/2x-6x

Answer 10

hmm shoot I got the numbers off

Answer 11

its okay

Answer 12

anyhow... you'd need to get the slopes first for each \(\large {
\begin{array}{ccllll}
x&y
\\\hline\\
{\color{red}{ -3}}&{\color{blue}{ 5}}\\
{\color{red}{ 0}}&{\color{blue}{ 4}}
\end{array}\qquad
\begin{array}{ccllll}
x&y
\\\hline\\
{\color{red}{ 0}}&{\color{blue}{ 4}}\\
{\color{red}{ 6}}&{\color{blue}{ 2}}
\end{array}\qquad
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
}\)

Answer 13

if the slopes are equal, no solution, or infinite solutions

if they differ, then 1 solution

Answer 14

i understand that i just dont understand slope

Answer 15

well... if you have not covered slopes yet... how are you meant to find whether they have solution or not then? that is, what is the chapter section covering to do so?