Answer:
The system of equations she could write is:
y = -x² + 4x
y = x - 4
The solutions are (-1 , -5) and (4 , 0)
Step-by-step explanation:
-x² + 4x = x - 4
That means two equations one quadratic which is in the left hand side and the other is linear which is in the right hand side.
They represented graphically by a parabola and a line, the solution of it will be the points of intersection of the two graphs
To find the system of equations take each side and equate it by y
∵ y = -x² + 4x
∵ y = x - 4
∴ The system of equations is:
y = -x² + 4x
y = x - 4
Let us solve this system using -x² + 4x = x - 4
∵ -x² + 4x = x - 4
- Subtract x from both sides
∴ -x² + 3x = -4
- Add 4 to both sides
∴ -x² + 3x + 4 = 0
- Multiply both sides by -1
∴ x² - 3x - 4 = 0
Let us use the factorization to solve it
∵ x² = (x)(x)
∵ -4 = (1)(-4)
∵ (x)(1) = x
∵ (x)(-4) = -4x
∵ x + -4x = - 3x ⇒ middle term
∴ The factors of x² - 3x - 4 are (x + 1)(x - 4)
- Substitute x² - 3x - 4 by its factors
∴ (x + 1)(x - 4) = 0
Equate each factor by 0 to find the values of x
∵ x + 1 = 0
- Subtract 1 from both sides
∴ x = -1
∵ x - 4 = 0
- Add 4 to both sides
∴ x = 4
Substitute the values of x in the equation y = x - 4 to find y
∵ y = -1 - 4
∴ y = -5
∵ y = 4 - 4
∴ y = 0
The solutions are (-1 , -5) and (4 , 0)
