Question

How many solutions does this system of equations have( one, no, infinitely many){y+2/3x=4{2x=12-3y

Answer 1

Answer:

The system has infinitely many solutions

Explanation:

We will try to solve the system, so:

If we isolate y on the first equation, we get:

y = 4 - (2/3)x

So, replacing y on the second equation and solving for x, we get:

$\begin{gathered} 2x=12-3y \\ 2x=12-3(4-\frac{2}{3}x) \\ 2x=12-(3\cdot4)+(3\cdot\frac{2}{3}x) \\ 2x=12-12+2x \\ 2x=2x \end{gathered}$

Since we get an identity, the system of equations has infinitely many solutions.