Solve the following linear and quadratic systems of equations:y + 3x = -2 or 3x +2 = yy = x^2a. Show all work in solving your system of equations algebraically.b. Graph your system of equations and show the solution graphically to verify your solution.

Solve the following linear and quadratic systems of equations:

$y={x}^{2}$
a. Show all work in solving your system of equations algebraically.
b. Graph your system of equations and show the solution graphically to verify your solution.

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Given Data:
Linear equation: $y=3x+2$ ……(1)
Quadratic equation: $y=x2$ ……(2)
(a)
Substitute x2 for y in the linear equation and solve
$y=3x+2$
${x}^{2}=3x+2$
${x}^{2}-3x-2=0$
$x=\left(-\left(-3\right)±\sqrt{\left(-3{\right)}^{2}-4\left(1\right)\left(-2\right)\right)/\left(2\left(1\right)}$
$x=3±\sqrt{17}/2$
$x=3.562$ and $x=0.562$
substitute 3.562 for x in equation 2
$y={x}^{2}$
$y=\left(3.562{\right)}^{2}$
$y=12.685$substitute -0.562 for x in equation 2
$y={x}^{2}$
$y=\left(-0.562{\right)}^{2}$
$y=0.315$
From above, the intersection points of line and curve are (-0.562, 0.315) and (3.562, 12.685).
(b)
The graph of line and curve is shown in the figure below.