Answer:
x = -4, y = -4
Step-by-step explanation:
Normally, if it's allowed, I would use a graphing calculator which basically turns the equations (-2x+y=4) and (y=[tex]\frac{1}{2}[/tex]x-2) into two straight lines, which represent the line of possible values that can fit into the equations. However, since you want the value of x and y in both equations to be the same, you have to look for the intersection of the two graphs. I use desmos.com/calculator to just type in the equations and the lines would be drawn automatically. By hovering over the equation, I can get the two values of x and y (the first value is for x, and the second one is for y).
Here is the working if you want to work it out by hand: (I'm using algebra for this one)
-2x+y=4 -------------------------------- Equation 1
y=[tex]\frac{1}{2}[/tex]x-2 ---------------------------------- Equation 2
Substitute Equation 2 into Equation 1:
-2x+[tex]\frac{1}{2}[/tex]x-2=4
Simplify:
-1[tex]\frac{1}{2}[/tex]x-2=4
-1[tex]\frac{1}{2}[/tex]x=4+2
-1[tex]\frac{1}{2}[/tex]x=6
1[tex]\frac{1}{2}[/tex]x=-6
[tex]\frac{3}{2}[/tex]x=-6
3x=-6×2
3x=-12
x=-12÷3
x=-4 ------------------------------------ Equation 3
Substitute Equation 3 into Equation 1:
-2(-4)+y=4
Simplify:
8+y=4
y=4-8
y=-4
Thus, x=-4, y=-4
