Solve by elimination method.
7r-3s=14
3r+7s=64
Could never figure out the elimination method. Would love some help with this one. Thanks
21r - 9s = 42
(I multiplied the first eq. by 3)
21r + 49s = 448
(I multiplied the second equation by 7)
58s = 406
(I subtracted the third equation from the fourth, to eliminate r.)
The remaining steps are easy.
s = 7
7r -21 = 14
r = 5
To solve this system of equations using the elimination method, we need to eliminate one of the variables by multiplying one or both of the equations by a constant. Here's how you can do it step by step:
1. Start with the given system of equations:
7r - 3s = 14 ---(Equation 1)
3r + 7s = 64 ---(Equation 2)
2. Multiply Equation 1 by 7 and Equation 2 by 3 to make the coefficient of "r" in both equations equal:
(7r - 3s) * 7 = 14 * 7 ---(Multiply Equation 1 by 7)
(3r + 7s) * 3 = 64 * 3 ---(Multiply Equation 2 by 3)
Simplifying these equations, we get:
49r - 21s = 98 ---(Equation 3)
9r + 21s = 192 ---(Equation 4)
3. Now, add Equation 3 and Equation 4 together to eliminate the "s" variable:
(49r - 21s) + (9r + 21s) = 98 + 192
Simplifying the equation, we get:
58r = 290
4. Divide both sides of the equation by 58 to solve for "r":
58r/58 = 290/58
r = 5
5. Substitute the value of "r" back into either Equation 1 or Equation 2 (let's use Equation 1):
7(5) - 3s = 14
Simplifying this equation, we get:
35 - 3s = 14
6. Solve for "s":
Subtract 35 from both sides of the equation:
-3s = 14 - 35
-3s = -21
Divide both sides of the equation by -3:
s = -21 / -3
s = 7
7. Therefore, the solution to the system of equations is r = 5 and s = 7.
By following these steps, you have successfully solved the system of equations using the elimination method.