# SOLUTION: 40x+26y=486.70 20x+31y=332.42

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 Question 269013: 40x+26y=486.70 20x+31y=332.42Found 2 solutions by persian52, checkley77:Answer by persian52(158)   (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(12569)   (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