Can someone please help with this problem?
Solve by the elimination method.
7r-9s= -58
9r+7s=74
I know that I need to multiply the first equation by 9 and the second equation by 7.
The equations look like this:
63r-81s= -522
63r+49s=518
After this I get confused. Could someone please help?
Thanks.
subtract
0r-130s=-1040
But how would I solve for r?
s=8 does that mean r=0?
Thanks.
Never mind I got the answer for r.
Thanks.
Of course! I'll be happy to help you solve this problem using the elimination method.
To eliminate one variable, we need to multiply one of the equations by a number such that when we add or subtract the two equations, one of the variables cancels out. In this case, you correctly multiplied the first equation by 9 and the second equation by 7, resulting in:
63r - 81s = -522 (Equation 1)
63r + 49s = 518 (Equation 2)
Now, to eliminate the "r" variable, we need to subtract Equation 2 from Equation 1. This will result in the "r" variable canceling out:
(63r - 81s) - (63r + 49s) = -522 - 518
Simplifying the equation:
63r - 81s - 63r - 49s = -1,040
Combining like terms:
-81s - 49s = -1,040
Now, combine the like terms on the left side of the equation:
-130s = -1,040
To solve for "s," divide both sides of the equation by -130:
s = -1,040 / -130
Simplifying:
s = 8
Now that we have obtained the value of "s," we can substitute it back into either Equation 1 or Equation 2. Let's use Equation 1:
7r - 9s = -58
Substituting s = 8:
7r - 9(8) = -58
Simplifying:
7r - 72 = -58
Now, isolate the "r" variable by adding 72 to both sides of the equation:
7r = -58 + 72
Simplifying:
7r = 14
Finally, solve for "r" by dividing both sides of the equation by 7:
r = 14 / 7
Simplifying:
r = 2
Therefore, the solution to the system of equations is r = 2 and s = 8.