need help figuring out this problem

short answer:
[input]solve( y=1/(2x)+1, y=-3x+8 )[/input]

long answer:
y=1/2x+1
y=-3x+8

1/(2x)+1=-3x+8 |-1
1/(2x) = -3x+7 |*2x
1 = (-3x+7)*2x
1 = -3x*2x+7*2x
1 = -6x^2+14x |-1
-6x^2+14x-1=0
p-q-formula (quadratic formula)
=> {x=0.073760245949667, x=2.259573087383667}

now insert both "x" in one of your equations:
=> {y=1.221280737849, y=7.778719262151}

Multiply top equation by 6, add two equations.

7y = 14

y = 2

$y=\frac{1}{2}x+1\\ y= -3x+8$_------(2)^------(1)

(1)-(2): 0 = $\frac{7}{2}x-7$

        $\frac{7}{2}x=7\\x=2$

 

$y = (\frac{1}{2})(2)+1\\y=1+1\\y=2$