Question

Solve the system of equations:y = 2x - 3y = x² - 3OA. (-1,-5) and (4, 5)OB. (3,6) and (-3, 6)OC. (0, -3) and (2, 1)OD. (0, 3) and (2,0)

Answer 1

The system of equations is solved by setting the two equations equal to each other, factoring the resulting quadratic equation, and finding the x values that satisfy it. These x values are then used to find the corresponding y values, resulting in the solutions (0, -3) and (2, 1).

Step-by-step explanation:

Step-by-Step Solution to the System of Equations

To solve the system of equations, we need to find values of x and y that satisfy both equations simultaneously. The two equations given are:

1. y = 2x - 3
2. y = x² - 3

Now we will set the two equations equal to each other since they both equal y:

2x - 3 = x² - 3

By moving all terms to one side, we get a quadratic equation:

x² - 2x = 0

We can factor out x:

x(x - 2) = 0

This gives us two possible solutions for x:

1. x = 0
2. x = 2

We will now substitute these values back into y = 2x - 3 to find the corresponding y values:

• For x = 0, y = 2(0) - 3 = -3
• For x = 2, y = 2(2) - 3 = 1

Therefore, the solutions to the system of equations are (0, -3) and (2, 1).