Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your gra
which of the following points represents a reasonable solution to the system of equations?
$y = 4x^2 - 6x + 2$
$y = \frac{2}{3}x + 1$
(1 point)
\\(\circ\\) (1,0)
\\(\circ\\) (0.167,2)
\\(\circ\\) (1.5,2)
\\(\circ\\) (0,1)

Explanation:

Step1: Substitute (1,0)

Substitute \(x = 1\), \(y = 0\) into \(y = 4x^2 - 6x + 2\): \(4(1)^2 - 6(1) + 2 = 4 - 6 + 2 = 0\). Substitute into \(y=\frac{2}{3}x + 1\): \(\frac{2}{3}(1)+1=\frac{5}{3}
eq0\). Not a solution.

Step2: Substitute (0.167,2)

\(x\approx0.167\), substitute into \(y = 4x^2 - 6x + 2\): \(4(0.167)^2 - 6(0.167)+2\approx4(0.0279)-1.002 + 2\approx0.1116 - 1.002+2\approx1.1096
eq2\). Not a solution.

Step3: Substitute (1.5,2)

Substitute \(x = 1.5\), \(y = 2\) into \(y = 4x^2 - 6x + 2\): \(4(1.5)^2 - 6(1.5)+2 = 4(2.25)-9 + 2 = 9 - 9 + 2 = 2\). Substitute into \(y=\frac{2}{3}x + 1\): \(\frac{2}{3}(1.5)+1 = 1 + 1 = 2\). Both equations satisfy.

Step4: Substitute (0,1)

Substitute \(x = 0\), \(y = 1\) into \(y = 4x^2 - 6x + 2\): \(4(0)^2 - 6(0)+2 = 2
eq1\). Not a solution.

Answer:

(1.5, 2)