Question

Solve the system of equations. Show your work.
y = x^2 -3x +4
x + y = 4

Answer 1

x + y = 2 , y = x 2 − 4 x + 4

Replace all occurrences of

y

with x 2 − 4 x + 4

in each equation.

x 2 − 3 x + 4 = 2 y = x 2 − 4 x + 4

Solve for

x

in the first equation.

x = 2 , 1 y = x 2 − 4 x+ 4

Replace all occurrences of

x with 2

in each equation.

y=0 x = 2

Replace all occurrences of x

with 1

in each equation.

y = 1 x = 1

The solution to the system is the complete set of ordered pairs that are valid solutions.

( 2 , 0 ) ( 1 , 1 )

The result can be shown in multiple forms.

Point Form:

( 2 , 0 ) , ( 1 , 1 )

Equation Form:

x=2 , y = 0 x = 1 , y = 1

Explanation: