Question

How many solutions does the system have?

3x + 12y = 20
y = –1/4 x + 5/3

Answer 1

Do you know how to solve systems such as this?

Answer 2

Hint: multiply\[y=\frac{-x}{4}+\frac{5}{3}\]by 12.

Answer 3

If \[\Large{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}\]
Then it has INFINITELY MANY solutions.

\[\Large{\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}}\]
Then it has NO solutions.

\[\Large{\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}}\]
Then it has only ONE solution.

Answer 4

Here,
\[\Large{\color{red}{a_1=3, a_2=\dfrac{-1}{4}, b_1=12, b_2=1, c_1=20, c_2=\dfrac{5}{3}.}}\]

Answer 5

oh alright i think i see