Question 269165: Solve this equation using the elimination method.
5x - 3y = 24
3x + 5y = 28
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! Here's a detail steps for solving the equation! ☺
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5x-3y=24_3x+5y=28
Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 15.
5*(5x-3y=24)_3*(3x+5y=28)
Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 15.
5*(5x-3y)=5(24)_3*(3x+5y)=3(28)
Multiply 5 by each term inside the parentheses.
5*(5x-3y)=120_3*(3x+5y)=3(28)
Multiply 5 by each term inside the parentheses.
(25x-15y)=120_3*(3x+5y)=3(28)
Remove the parentheses around the expression 25x-15y.
25x-15y=120_3*(3x+5y)=3(28)
Multiply 3 by each term inside the parentheses.
25x-15y=120_3*(3x+5y)=84
Multiply 3 by each term inside the parentheses.
25x-15y=120_(9x+15y)=84
Remove the parentheses around the expression 9x+15y.
25x-15y=120_9x+15y=84
Add the two equations together to eliminate y from the system.
9x+15y=84_25x-15y=120_34x =204
Divide each term in the equation by 34.
x=6
Substitute the value found for x into the original equation to solve for y.
25(6)-15y=120
Multiply 25 by each term inside the parentheses.
150-15y=120
Move all terms not containing y to the right-hand side of the equation.
-15y=-30
Divide each term in the equation by -15.
y=2
This is the final solution to the independent system of equations.
Answer: x=6
Answer: y=2
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