solve each system by substitution - 2x + 2y = 2, -4x + 4y = 12
Having difficulties solving this equation substituion. Please help.
Looking at these equations should tell you that they represent
parallel lines. Multiply the first equation by 2 and you get
-4x + 4y = 4. Now, both equations have exactly the same
values on the left side, but different values on the right side.
Re-work both equations so they are in standard y = mx + b
form, and you find that both lines have the same slope. They
never intersect, therefore there is no co-ordinate pair of x, y
that will solve both equations.
Let's proceed anyway. Solve equation one for x in terms of y.
- 2x + 2y = 2
-2x = -2y + 2
x = y - 1
Substitute that value of x into the second equation.
-4x + 4y = 12
-4(y - 1) + 4y = 12
-4y + 4 + 4y = 12
The -4y and + 4y cancel each other out, leaving
4 = 12, which is not true.