Q:

# solve the system of equations y=x^2+3-6 y=2x-6

Accepted Solution

A:
The solutions of the system of equations are (0 , -6) , (-1 , -8)Step-by-step explanation:To solve a system of equations, one 1st degree and the other 2nd degree, do that:Use the 1st degree equation to find one variable in terms of other variableSubstitute this variable in the 2nd degree equation and solve it to find the other variableSubstitute the value of the other variable in the 1st degree equation to find the first variable∵ The system of equations is:y = x² + 3x - 6 ⇒ (1)y = 2x - 6 ⇒ (2)Equate (1) and (2)∴ x² + 3x - 6 = 2x - 6- Add 6 to both sides∴ x² + 3x = 2x- Subtract 2x from both sides∴ x² + x = 0- Take x as a common factor in the left hand side∴ x(x + 1) = 0- Equate each factor by 0 to find the values of x∵ x = 0∴ The first value of x is 0∵ x + 1 = 0- Subtract 1 from each side∴ x = -1∴ The second value of x is -1Substitute each value of x in equation (2) to find the values of y∵ y = 2(0) - 6∴ y = 0 - 6 = -6The first value of y is -6∵ y = 2(-1) - 6∴ y = -2 - 6 = -8∴ The second value of y is -8∴ The solutions are (0 , -6) , (-1 , -8)The solutions of the system of equations are (0 , -6) , (-1 , -8)Learn more:You can learn more about the system of equations in brainly.com/question/3739260#LearnwithBrainly