Question

Solve the following system of equations and show all work.

y = 2x2
y =
3x -1 (10 points)

Answer 1

Answer:
`\left((1)/(2), 1 \right), (1, 2)`

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=(1)/(2), 1`

If
`x=(1)/(2)`, then
`y=3\left((1)/(2) \right)-1=1`

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

Therefore, the solutions are
`\left((1)/(2), 1 \right), (1, 2)`