We can solve the system of equations by elimination. To do this, we will multiply both sides of the second equation by 5 and both sides of the first equation by 3 to get the same coefficient for y in both equations:
3(3x-5y) = 3(29)
5(2x+3y) = 5(-6)
This simplifies to:
9x - 15y = 87
10x + 15y = -30
Now we can add the two equations together:
(9x - 15y) + (10x + 15y) = 87 + (-30)
This simplifies to:
19x = 57
Dividing both sides by 19, we get:
x = 3
Now we can substitute x = 3 into one of the original equations to solve for y. Let's use the first equation:
3(3) - 5y = 29
Simplifying:
9 - 5y = 29
Subtracting 9 from both sides:
-5y = 20
Dividing both sides by -5, we get:
y = -4
Therefore, the solution to the system of equations is x = 3 and y = -4.
Solve the systems of equations by elimination
3x-5y = 29
2x+3y = -6
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