3x- 5y/(7 ) = 10
2x/3 - 9y/7 = 19/5
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THE RODDER THOUGHT THAT A GREAT BLACK MONSTER HAD HIT HIM WITH A CLUD.WHAT REALLY HAPPENED
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To solve this system of equations, we can use the method of substitution. Here are the steps to solve it:
Step 1: Rearrange the first equation to solve for x in terms of y.
3x - 5y/7 = 10
Multiply both sides by 7: 21x - 5y = 70
Add 5y to both sides: 21x = 5y + 70
Divide both sides by 21: x = (5y + 70)/21
Step 2: Substitute this expression for x into the second equation.
2x/3 - 9y/7 = 19/5
Substitute x: 2((5y + 70)/21)/3 - 9y/7 = 19/5
Step 3: Simplify the expression.
2(5y + 70)/63 - 9y/7 = 19/5
Multiply by the common denominator, which is 315: 10(5y + 70) - 81(9y) = 19(63)
Distribute and simplify: 50y + 700 - 729y = 1197
Combine like terms: -679y + 700 = 1197
Subtract 700 from both sides: -679y = 497
Divide both sides by -679: y = -497/679
Step 4: Substitute the value of y back into the expression for x.
x = (5y + 70)/21
x = (5(-497/679) + 70)/21
Step 5: Simplify the expression.
x = (-2485/679 + 4930/679)/21
x = 2445/14359
Therefore, the solution to the system of equations is x = 2445/14359 and y = -497/679.