SOLUTION: I can't get the answer to the following problem ; y-5x=-2 3x-7y=22 The instructions say to use the substitution method.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I can't get the answer to the following problem ; y-5x=-2 3x-7y=22 The instructions say to use the substitution method.       Log On


   



Question 734890: I can't get the answer to the following problem ;
y-5x=-2
3x-7y=22
The instructions say to use the substitution method.

Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y-5x=-2 --> y = 5x - 2
3x-7y=22
----------
Sub for y in the 2nd equation.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Substitution means that your first step is solving for one variable in one of the equations. For example
y-5x=-2 --> y=5x-2
Note: Look for a variable that has no visible coefficient. In this case, the coefficient of y in y-5x=-2 is an invisible number 1.

The second step when using substitution is to substitute the expression found for the variable in the other equation.
In this case, since we found that y=5x-2, we write (5x-2) instead of y in 3x-7y=22 to get
3x-7%285x-2%29=22
No we use the distributive property to transform that into
3x-7%2A%285x%29-7%2A%28-2%29=22 and simplify to 3x-35x%2B14=22 and -32x%2B14=22
Then we solve -32x%2B14=22
-32x%2B14=22 --> -32x=22%7D-14%7D%7D+--%3E+%7B%7B%7B-32x=8 --> x=8%2F%28-32%29 --> highlight%28x=-1%2F4%29

As a final step, we substitute -1%2F4 for x somewhere to find y.
It may be easiest to use y=5x-2. Substituting we get
y=5%28-1%2F4%29-2--> y=-5%2F4-2 --> y=-5%2F4-8%2F4 --> highlight%28y=-13%2F4%29

NOTE: If you cannot find a variable with no visible coefficient, substitution will get cumbersome, as you would be working with fractions a lot. In that case, it is better to use a different method.