Solve using elimination.–3x + 10y = –15–2x + 9y = –17

Sure, let's solve the system of equations using elimination.

The system of equations is:

-3x + 10y = -15 ...(1)

-2x + 9y = -17 ...(2)

The goal is to eliminate one of the variables (either x or y). We can do this by multiplying each equation by a suitable number so that the coefficients of x or y in both equations will be the same.

Let's multiply equation (1) by 2 and equation (2) by 3:

-6x + 20y = -30 ...(3)

-6x + 27y = -51 ...(4)

Now, we can subtract equation (4) from equation (3) to eliminate x:

-6x - (-6x) = -6x + 6x = 0

20y - 27y = -7y

-30 - (-51) = -30 + 51 = 21

So, the resulting equation is -7y = 21.

To solve for y, divide both sides of the equation by -7:

y = 21 / -7 = -3

Now that we have y, we can substitute it into either of the original equations to solve for x. Let's substitute y = -3 into equation (1):

-3x + 10(-3) = -15

-3x - 30 = -15

-3x = -15 + 30 = 15

x = 15 / -3 = -5

So, the solution to the system of equations is x = -5, y = -3.