x+14y=84 2x-7y=-7
2x-7y=-7
2x+7=7y
x+3.5=3.5y
x=0 y=1
x+14y=84
14y=84-x
x=0 y=6
this is how i just figured it out...
x+14y=84
2x-7y=-7
.....
-7(x+14y=84)
14(2x-7y=-7)
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7x+98y=588
+28x-98y=-98
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35x =490
----- ----
35 35
x=14
then i solved for y.
To find the solution to this system of linear equations, you can use the method of substitution or the method of elimination. Let's use the method of elimination to solve the system:
Given equations:
1) x + 14y = 84
2) 2x - 7y = -7
First, let's eliminate one variable. We can eliminate the variable "x" by multiplying equation (1) by 2 and equation (2) by 1:
Multiply equation (1) by 2:
2(x + 14y) = 2(84)
2x + 28y = 168
Multiply equation (2) by 1:
1(2x - 7y) = 1(-7)
2x - 7y = -7
Now, subtract equation (2) from equation (1) to eliminate "x":
(2x + 28y) - (2x - 7y) = 168 - (-7)
2x - 2x + 28y + 7y = 168 + 7
35y = 175
Now, solve for "y" by dividing both sides of the equation by 35:
35y/35 = 175/35
y = 5
Substitute the value of "y" back into one of the original equations (equation 1) to solve for "x":
x + 14y = 84
x + 14(5) = 84
x + 70 = 84
x = 84 - 70
x = 14
So, the solution to the system of equations is x = 14 and y = 5.
To check the solution, substitute x = 14 and y = 5 back into both original equations and verify that they hold true.