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Solve the following system of equations.

y = –5x + 3
y = 2x2 – x – 3


A) (1,–2), (3,–12)

B) (–1,8), (–3,18)

C) (–1,8), (3,12)

D) (1,–2), (–3,18)

User TAB
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1 Answer

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AI-generated answer

To solve the system of equations:

y = -5x + 3

y = 2x^2 - x - 3

We can use the method of substitution or elimination. Let's use the substitution method in this case.

Step 1: Solve one equation for one variable in terms of the other variable.

From the first equation, we can solve for y:

y = -5x + 3

Step 2: Substitute the expression for y into the other equation.

Replace y in the second equation with the expression -5x + 3:

-5x + 3 = 2x^2 - x - 3

Step 3: Rearrange the equation into standard form.

Move all terms to one side to get a quadratic equation:

2x^2 - x + 5x - 6 = 0

2x^2 + 4x - 6 = 0

Step 4: Solve the quadratic equation.

We can either factor, complete the square, or use the quadratic formula to solve the equation. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 4, and c = -6.

x = (-4 ± √(4^2 - 4(2)(-6))) / (2(2))

x = (-4 ± √(16 + 48)) / 4

x = (-4 ± √64) / 4

x = (-4 ± 8) / 4

This gives us two possible solutions for x:

x1 = (-4 + 8) / 4 = 1

x2 = (-4 - 8) / 4 = -3

Step 5: Substitute the values of x into one of the original equations to find the corresponding y values.

Using the first equation, let's substitute x = 1:

y = -5(1) + 3

y = -5 + 3

y = -2

Using the first equation again, let's substitute x = -3:

y = -5(-3) + 3

y = 15 + 3

y = 18

So, the solutions to the system of equations are:

(x, y) = (1, -2) and (-3, 18)

These are the points where the two equations intersect on the coordinate plane.

User Anne Lacan
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