Solve by the elimination method. Is there a solution?

2r-5s= -11
5r+2s= 16

Try to get rid of the r first. Multiply the top row by -5 and the bottom row by 2. solve for s.

Get rid of the s next, multiplying the top by 2 and the bottom by 5. solve for r.

There should be a solution.

3r-4s=3

4r+3s=39

To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. Let's start by eliminating the "s" variable.

To do this, we'll multiply the first equation by 2 and the second equation by 5 to make the coefficients of "s" the same.

Equation 1: 2r - 5s = -11
Equation 2: 5r + 2s = 16

Multiply Equation 1 by 2:
4r - 10s = -22

Multiply Equation 2 by 5:
25r + 10s = 80

Now, we can add the two equations together to eliminate the "s" variable:

(4r - 10s) + (25r + 10s) = -22 + 80
4r + 25r - 10s + 10s = 58
29r = 58

Now, we can solve for "r" by dividing both sides by 29:
r = 58/29
r = 2

Now that we have the value of "r," we can substitute it back into one of the original equations to solve for "s." Let's use the first equation:

2r - 5s = -11
2(2) - 5s = -11
4 - 5s = -11
-5s = -11 - 4
-5s = -15
s = -15 / -5
s = 3

So, the solution to the system of equations is r = 2 and s = 3.

Therefore, there is a unique solution to the system of equations.