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 variable
- Substitute this variable in the 2nd degree equation and solve it to find the other variable
- Substitute 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 -1
Substitute each value of x in equation (2) to find the values of y
∵ y = 2(0) - 6
∴ y = 0 - 6 = -6
The 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
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