The solutions of the system of equations are (0 , 13) , (3 , 34)
Step-by-step explanation:
To solve an system of equations, one of them linear and the other is quadratic do that
- Use the linear equation to find one variable in terms of the other variable
- Substitute this variable in the quadratic equation
- Solve the quadratic equation to find the values of the other variable
- Substitute the values of the other variable in the linear equation to find the first variable
The system of equation is:
y = x² + 4x + 13 ⇒ (1)
y = 7x + 13 ⇒ (2)
Substitute y in equation (1) by equation (2)
x² + 4x + 13 = 7x + 13
Subtract 13 from both sides
∴ x² + 4x = 7x
Subtract 7x from both sides
x² - 3x = 0
Take x as a common factor
x(x - 3) = 0
Equate each factor by 0
x = 0
x - 3 = 0
Add 3 to both sides
x = 3
The values of x are 0 and 3
Substitute the values of x in equation (2) to find y
When x = 0
y = 7(0) + 13
y = 0 + 13
y = 13
When x = 3
y = 7(3) + 13
y = 21 + 13
y = 34
The values of y are 13 and 34
The solutions of the system of equations are (0 , 13) , (3 , 34)
Learn more:
You can learn more about the system of equations in brainly.com/question/3739260
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