Solve by elimination method.

2r-5s=-33
5r+2s=48

I keep getting different answers... I can never get these right.... so first I multiply the first equation by 2 and the second by 5?

can someone please check my answer?

the answer I got was s= -69/-21 or 3.28

By what can you multiply that would cause one of the variable letters to drop out? Positive 10 of whatever plus negative 10 of whatever else would do the job. Your first inclination was pretty much right on the money. Make sure to multiply whatever you use all the way across.

To solve the system of equations using the elimination method, you need to eliminate one variable by adding or subtracting the equations.

Let's go step by step:

1. Multiply the first equation by 2 and the second equation by 5 to make the coefficients of the "r" terms equal:

Equation 1: 2r - 5s = -33
Multiply both sides by 2:
4r - 10s = -66

Equation 2: 5r + 2s = 48
Multiply both sides by 5:
25r + 10s = 240

2. Now, add the two equations together, which eliminates the "s" term.

(4r - 10s) + (25r + 10s) = (-66) + (240)
Combining like terms:
29r = 174
Divide both sides by 29:
r = 6

3. Substitute the value of "r" (which is 6) into one of the original equations to solve for "s."

Using Equation 1:
2(6) - 5s = -33
12 - 5s = -33
Subtract 12 from both sides:
-5s = -45
Divide both sides by -5:
s = 9

So, the solution to the system of equations is r = 6 and s = 9.

Make sure to check your answer by substituting the values back into the original equations, as mistakes can occur during calculations.