 # 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. Tazmin Horton 2020-10-19 Answered

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. 