2r-9s=-24
9r+2s=62
the quest asks to write a order pair or tell if there is infinitely solutions or no solutions. can you help
Yes, I can help you with that. To solve this system of equations, we can use either the substitution method or the elimination method. I'll guide you through the elimination method.
First, let's manipulate the equations to eliminate one of the variables. Let's multiply the first equation by 2 and the second equation by 9 to make the coefficients of "s" in both equations the same:
Equation 1: 2(2r-9s) = 2(-24) --> 4r - 18s = -48
Equation 2: 9(9r+2s) = 9(62) --> 81r + 18s = 558
Now, add the two equations together:
(4r - 18s) + (81r + 18s) = -48 + 558
Simplifying the equation:
85r = 510
Divide both sides by 85 to solve for "r":
r = 6
Now, substitute the value of "r" back into one of the original equations to solve for "s". Let's use Equation 1:
2r - 9s = -24
2(6) - 9s = -24
12 - 9s = -24
Subtract 12 from both sides:
-9s = -36
Divide both sides by -9 to solve for "s":
s = 4
Therefore, the ordered pair (r, s) is (6, 4).