How do you solve the system y = -x + 2y=x+2, 2y = 4 - 2x2y=42x?

1 Answer
Mar 5, 2018

(x,-x+2)(x,x+2)

Explanation:

y=-x+2color(white)(88)[1]y=x+288[1]

2y=4-2xcolor(white)(888)[2]2y=42x888[2]

We can solve this one by substitution. Notice we already know the value of yy in terms of xx from equation [1][1]. Substituting this in equation [2][2], give us:

2(-x+2)=4-2x2(x+2)=42x

-2x+4=4-2x2x+4=42x

0=00=0

This is known as linear dependence. What this means is we have two equations, but one is just a multiple of the other. Notice:

2y=4-2x2y=42x

Is just bb(y=-x+2) multiplied by bb2:

2(y=-x+2)

In this situation we have to assign an arbitrary value to one of the variables and express the other variable in terms of this. So for arbitrary x

y=-x+2

We can write the solutions as:

(x,y)->(x,-x+2)

Since we are assigning a value to x and calculating the corresponding value of y, this gives us an infinite number of solutions.

If these two equations are graphed we find that they are exactly the same line.