## anonymous 3 years ago How many solutions does the system have? 3x + 12y = 20 y = –1/4 x + 5/3

1. anonymous

Do you know how to solve systems such as this?

2. anonymous

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

3. TheViper

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.

4. TheViper

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

5. anonymous

oh alright i think i see