Solve by elimination method. Please show step by step process.
7r-4s=-7
4r+7s=61
multiply the top equation by 7, and the bottome equation by 4.
Then add the equations, which will eliminate the s variable.
I will be happy to critique your work
7r-4s=-7 (7)
4r+7s=61 (4)
49r - 28s = -49
16r + 28s = 244
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65r = 195
195/65 = 3 (simplified) (3, is the first number of the ordered pair.)
Now this is the part that I get lost on. I know I am suppose to substitute 3 into one of the equations above, but how do I determine which one. So if I substitute 3 into the 1st equation:
7(3)-4s= -7
21 - 4s= -7
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21 = -7 would my answer be -7/21
Substitute 3 into the 2nd equation:
4(3)+7s = 61
12 + 7s = 61
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12 = 61 would my answer be 61/12
(3, is the first number of the ordered pair.)
(3,-7/21) or (3,61/12) which ordered pair is correct?
To solve the given system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by suitable numbers, so that when we add or subtract the two equations, one of the variables cancels out.
Step 1: Multiply the first equation by 4 and the second equation by 7 to make the coefficients of the variable "s" equal in magnitude.
4 * (7r - 4s) = 4 * (-7)
7 * (4r + 7s) = 7 * 61
Simplifying the equations, we get:
28r - 16s = -28 --> Equation 1
28r + 49s = 427 --> Equation 2
Step 2: Now, subtract Equation 1 from Equation 2 to eliminate the "r" variable.
(28r + 49s) - (28r - 16s) = 427 - (-28)
Simplifying the equation, we get:
65s = 455
Step 3: Divide both sides of the equation by 65 to solve for "s".
s = 455/65
s = 7
Step 4: Substitute the value of "s" back into one of the original equations to solve for "r".
7r - 4(7) = -7
Simplifying the equation, we get:
7r - 28 = -7
Step 5: Add 28 to both sides of the equation to isolate "r".
7r = 21
Step 6: Divide both sides of the equation by 7 to solve for "r".
r = 21/7
r = 3
So, the solution to the system of equations is r = 3 and s = 7.