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Question 269013: 40x+26y=486.70
20x+31y=332.42
Found 2 solutions by persian52, checkley77:
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 40x+26y=486.7_20x+31y=332.42
►Since 26y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 26y from both sides.
40x=-26y+486.7_20x+31y=332.42
►Divide each term in the equation by 40.
(40x)/(40)=-(26y)/(40)+(486.7)/(40)_20x+31y=332.42
►Simplify the left-hand side of the equation by canceling the common terms.
x=-(26y)/(40)+(486.7)/(40)_20x+31y=332.42
►Combine the numerators of all expressions that have common denominators.
x=(-26y+486.7)/(40)_20x+31y=332.42
►Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is ((-26y+486.7))/(40).
x=(-26y+486.7)/(40)_20((-26y+486.7)/(40))+31y=332.42
►Remove the parentheses around the expression -26y+486.7.
x=(-26y+486.7)/(40)_20((-26y+486.7)/(40))+31y=332.42
►Divide each term in the numerator by the denominator.
x=-(26y)/(40)+(486.7)/(40)_20((-26y+486.7)/(40))+31y=332.42
►Reduce the expression -(26y)/(40) by removing a factor of 2 from the numerator and denominator.
x=-(13y)/(20)+(486.7)/(40)_20((-26y+486.7)/(40))+31y=332.42
►Divide 486.7 by 40 to get 12.17.
x=-(13y)/(20)+12.17_20((-26y+486.7)/(40))+31y=332.42
►Remove the parentheses around the expression -26y+486.7.
x=-(13y)/(20)+12.17_20((-26y+486.7)/(40))+31y=332.42
►Divide each term in the numerator by the denominator.
x=-(13y)/(20)+12.17_20(-(26y)/(40)+(486.7)/(40))+31y=332.42
►Reduce the expression -(26y)/(40) by removing a factor of 2 from the numerator and denominator.
x=-(13y)/(20)+12.17_20(-(13y)/(20)+(486.7)/(40))+31y=332.42
►Divide 486.7 by 40 to get 12.17.
x=-(13y)/(20)+12.17_20(-(13y)/(20)+12.17)+31y=332.42
►Multiply 20 by each term inside the parentheses.
x=-(13y)/(20)+12.17_(-13y+243.35)+31y=332.42
►Since -13y and 31y are like terms, subtract 31y from -13y to get 18y.
x=-(13y)/(20)+12.17_18y+243.35=332.42
►Since 243.35 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 243.35 from both sides.
x=-(13y)/(20)+12.17_18y=-243.35+332.42
►Add 332.42 to -243.35 to get 89.07.
x=-(13y)/(20)+12.17_18y=89.07
►Divide each term in the equation by 18.
x=-(13y)/(20)+12.17_(18y)/(18)=(89.07)/(18)
►Simplify the left-hand side of the equation by canceling the common terms.
x=-(13y)/(20)+12.17_y=(89.07)/(18)
►Divide 89.07 by 18 to get 4.95.
x=-(13y)/(20)+12.17_y=4.95
►Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 4.95.
x=-(13(4.95))/(20)+12.17_y=4.95
►Multiply -13 by 4.95 in the numerator.
x=(-13*4.95)/(20)+12.17_y=4.95
►Multiply -13 by 4.95 to get -64.33.
x=(-64.33)/(20)+12.17_y=4.95
►Move the minus sign from the numerator to the front of the expression.
x=-(64.33)/(20)+12.17_y=4.95
►Divide -64.33 by 20 to get -3.22.
x=-3.22+12.17_y=4.95
►Add 12.17 to -3.22 to get 8.95.
x=8.95_y=4.95
►This is the solution to the system of equations.
=► x=8.95_y=4.95
Answer by checkley77(12844)  (Show Source):
You can put this solution on YOUR website! 20x+31y=332.42 multiply by -2 & add.
40x+26y=486.70
-40x-62y=-664.84
------------------
-36y=-178.14
y=-178.14/-36
y=29.69/6 ans.
20x+31(29.69/6)=332.42
20x+920.39/6=332.42
20x=332.42-920.39/6
20x=(1,994.52-920.39)/6
20x=1,074.13/6
x=(1,074.13/6)/20
x=(1,074.13/6)1/20
x=1,074.13/120 ans.
Proof:
40(1,074.13/120)+26(29.69/6)=486.7
42,965.2/120+771.94/6=486.7
358.0433+128.6567=486.7
486.7=486.7
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