Question

Solve the following system of equations and show all work. y = 2x2 y = 3x -1 (10 points)

Answer 1

Answer: $\left(\frac{1}{2}, 1 \right), (1, 2)$

Step-by-step explanation:

We have $y=2x^{2}$ and $y=3x-1$.

Since both of the equations are set equal to y, we can conclude that:

$2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1$

If $x=\frac{1}{2}$, then $y=3\left(\frac{1}{2} \right)-1=1$

If $x=1$, then $y=3-1=2$

Therefore, the solutions are $\left(\frac{1}{2}, 1 \right), (1, 2)$