To solve this system of equations using the elimination method, we can multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same:
5 * (3x - 4y) = 5 * 40
3 * (5x - 5y) = 3 * 55
Which simplifies to:
15x - 20y = 200
15x - 15y = 165
Now, we can subtract the second equation from the first equation to eliminate x:
(15x - 20y) - (15x - 15y) = 200 - 165
This simplifies to:
-20y + 15y = 35
Combining like terms:
-5y = 35
Dividing both sides by -5:
y = -7
Now, we substitute this value back into one of the original equations to solve for x. Let's use the first equation:
3x - 4(-7) = 40
3x + 28 = 40
Subtracting 28 from both sides:
3x = 12
Dividing both sides by 3:
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.
Solve the system of equations. 3x−4y=40 5x−5y=55
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