SOLUTION: please help me to grasp the concept of solving with elimination method.
-3x+4y=1
-6+6y=-3
4x-8y=48
11x+3y=105.5
8x+11y=-50
-32x-44y=-200
Algebra ->
Expressions-with-variables
-> SOLUTION: please help me to grasp the concept of solving with elimination method.
-3x+4y=1
-6+6y=-3
4x-8y=48
11x+3y=105.5
8x+11y=-50
-32x-44y=-200
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You can put this solution on YOUR website! solving with elimination method.
-3x + 4y = 1
-6x + 6y =-3
the idea is to multiply one or both equations so that one variable has the same coefficient, ideally one is positive and the other negative
Multiply the 1st equation by -2, add to the 2nd equation
+6x - 8y = -2
-6x + 6y = -3
----------------Adding eliminates x, find y
0 + -2y = -5
y =
y = +2.5
;
find x using the 1st equation
-3x + 4(2.5) = 1
-3x + 10 = 1
-3x = 1 - 10
-3x = -9
divide both sides by -3
x = 3
:
Check our solution in the 2nd equation
-6x + 6y = -3
-6(3) + 6(2.5) = -3
-18 + 15 = -3
:
:
4x - 8y = 48
11x + 3y = 105.5
multiply the 1st equation by 3, the 2nd equation by 8
12x - 24y = 144
88x + 24y = 844
-----------------adding eliminates y, find x
100x + 0 = 988
x = 988/100
x = 9.88
:
Find y using the 1st equation
4(9.88) - 8y = 48
39.52 - 8y = 48
-8y = 48 - 39.52
-8y = 8.48
y =
y = -1.06
:
Check solution in the 2nd equation
11x + 3y = 105.5
11(9.88) + 3(-1.06) = 105.5
108.68 - 3.18 = 105.5
:
:
8x + 11y = -50
-32x -44y =-200
multiply the 1st equation by 4, add to the 2nd equation
+32x + 44y = -200
-32x -44y = -200
--------------
note that every term cancels, the two equations are equivalent, dependent
