Question

Solving Linear Equations - Elimination

Write whether each of these systems of equations has a common solution or not. Explain

y = -x + 2 Y = 2x + 1

If you show me one and explain it, then I can probably do the rest...Thanks

Answer 1

if both of your equations are expressed as y = ..., then they are easy to solve.
You simply equate the right sides, that is,
-x+2=2x+1
-3x = -1
x = 1/3

sub that back into either one of the two original equations to get the y
I does not matter which one, you will get the same answer,

so in the first
y = -(1/3) + 2 = 5/3

what you are doing is finding the intersection point,(the common solution), of your two lines.
It is (1/3,5/3)