1 of 101 of 10 Items Question Multiple Choice Solve the system of equations. y = 2x² – 3 y = 3x – 1 (1 point) Responses no solution no solution (–, 5), (2, –) (– Image with alt text: one-half , 5), (2, – Image with alt text: start fraction 5 over 2 end fraction ) (–, –), (2, 5) (– Image with alt text: one-half , – Image with alt text: start fraction 5 over 2 end fraction ), (2, 5) (, ), (2, 5) ( Image with alt text: one-half , Image with alt text: start fraction 5 over 2 end fraction ), (2, 5) Skip to navigation

1 answer

The correct answer is (1/2, 5), (2, 5).

To solve the system of equations, set the two equations equal to each other:

2x² – 3 = 3x – 1

Rearrange to set it equal to zero:

2x² - 3x + 2 = 0

Factor the equation:

(2x - 1)(x - 2) = 0

Set each factor equal to zero:

2x - 1 = 0
x = 1/2

x - 2 = 0
x = 2

Now that we have the x values, plug them back into one of the original equations to find the corresponding y values:

For x = 1/2:
y = 2(1/2)² - 3
y = 2(1/4) - 3
y = 1/2 - 3
y = -5/2

For x = 2:
y = 2(2)² - 3
y = 2(4) - 3
y = 8 - 3
y = 5

Therefore, the solution is (1/2, -5/2) and (2, 5).