Question 1208973: Without graphing, find the point of intersection of the lines -x+2y=-4 and 2x+y=3 Found 3 solutions by josgarithmetic, timofer, math_tutor2020:Answer by josgarithmetic(39617) (Show Source):
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The original system is
Let's say we wanted to eliminate the x variable. To do so, we can double both sides of the 1st equation to get this equivalent system
At this point the x coefficients are equal in magnitude but opposite sign.
Adding straight down has the x terms go to 0.
The y terms add to 5y. The right hand sides add to -5.
So 5y = -5 leads to y = -1
Then plug this into any equation mentioned so far. Isolate x.
-x+2y = -4
-x+2(-1) = -4
-x-2 = -4
-x = -4+2
-x = -2
x = 2
We have x = 2 pair up with y = -1
The ordered pair solution is (2, -1)
This is where the two lines intersect.
Let's isolate y in the 2nd equation
2x+y = 3 turns into y = -2x+3
That is then plugged into the other equation of the original system so we can solve for x.
-x+2y=-4
-x+2(-2x+3)=-4
-x-4x+6=-4
-5x+6=-4
-5x=-4-6
-5x=-10
x = -10/(-5)
x = 2
Then,
y = -2x+3
y = -2*2+3
y = -4+3
y = -1
We arrive at (x,y) = (2, -1) once again.
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