SOLUTION: Can you please help me by WALKING me through how we determine that the intesect points for these two equations is (3,-1): (x - y = 4) & (x + y = 2). I need to see each step in the

Question 175203: Can you please help me by WALKING me through how we determine that the intesect points for these two equations is (3,-1): (x - y = 4) & (x + y = 2). I need to see each step in the process of coming up with (3, -1). I know that these two points solves both equations. Thanks, Charlie
Found 2 solutions by Alan3354, actuary:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Can you please help me by WALKING me through how we determine that the intesect points for these two equations is (3,-1): (x - y = 4) & (x + y = 2). I need to see each step in the process of coming up with (3, -1). I know that these two points solves both equations. Thanks, Charlie
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You determine the "solution" for the system of the 2 eqns. The solution is the point, or the values that satisfy both eqns. In graphical terms, it's where the 2 lines cross (these are linear, so they're straight lines).
x - y = 4
x + y = 2
Solve by elimination and substitution, since the coeffs are all 1's.
Add the 2 eqns
2x + 0y = 6
x = 3
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Sub x into either eqn to find y, I'll use eqn 1.
3 - y = 4
y = -1
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Those 2 values are the point (3,-1)

Answer by actuary(112) (Show Source): You can put this solution on YOUR website!
(x - y = 4) & (x + y = 2).
Rewrite each equation to slope y-intercept form
x-y=4 Can be rewritten as y=x-4 (Equation #1)
x+y=2 Can be rewritten as y=2-x (Equation #2)
REplace equation #2 into Equation #1
so 2-x=x-4
Gather all like terms on the same side of the equation
So 2x=6
Solve for x
x=3
Substitute x=3 into Equation #2
y=2-3=-1
So the solution is (3,-1)
I hope that this helps. This is a general approach that should work with all similar problems.

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