Answer: x = 2, y = 2
Step-by-step explanation:
[tex]y=x^2-3x+4\\x + y = 4\quad \implies y=4-x\\\\\underline{\text{Substitute y (in the first equation) with 4 - x:}}\\4-x=(4-x)^2-3(4-x)+4\\\\\underline{\text{Expand and distribute right-hand side:}}\\4-x=16-8x+x^2-12+3x+4\\\\\underline{\text{Simplify right-hand side:}}\\4-x=8-5x+x^2\\\\\underline{\text{Set left-hand side equal to zero (subtract 4 and add x):}}\\0=4-4x+x^2\quad \implies 0=x^2-4x+4\\\\\underline{\text{Factor and solve for x:}}\\0=(x-2)(x-2)\\0=x-2\\2=x[/tex]
Replace x with 2 in the second equation to solve for y:
x + y = 4
2 + y = 4
y = 2
