What is the solution to the system of equations y = -x + 4 y= 1/2x + 1

Question

Math

Answer 1

-x+4 = (1/2)x +1

3x/3 = 3

x/3 = 1

x = 3

y = 1

or maybe you really did mean y =1/2x +1

then

-x+4 = 1/2x +1

-x= 1/2x -3

-2x^2 = 1 -6x

2x^2 -6x =-1

x^2 -3x = -1/2

x^2 -3x + 9/4 = -1/2 +9/4

(x-3/2)^2 = 7/4

x = 3/2 +/- sqr7)/2

x= (3+sqr7)/2 or (3-sqr7)/2

y =-x +4 = (-3+sqr7)/2 +4 or (-3+sqr7)/2 + 4

or maybe you even meant to write

y= 1/(2x+1), then

-x+4 = 1/(2x+1)

(-x+4)(2x+1) = 1

-2x^2 +9x +4 = 1

2x^2 -9x -3 =0

x = 9/4 +/-(1/4)sqr(81+12)

x = (9+sqr93)/4 or (9-sqr93)/4

y = (-9-sqr93)/4 +4 or (sqr93-9)/4 + 4

y = (7-sqr93)/4 or (sqr93 +7)/4

since the 1st solution comes out with integers

it's the likely solution you want

although technically the way the problem is written

the 2nd solution is correct, applying PEMDAS