Solve the systems of equations by elimination

3x-5y = 29
2x+3y = -6

1 answer

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.