SOLUTION: solve the following system bu substitution x=7y+9 x=7/4y what is the solution set? solve by the substitution method. x-y=-1 7x+3y=-67 what is the solution set?

Algebra ->  Radicals -> SOLUTION: solve the following system bu substitution x=7y+9 x=7/4y what is the solution set? solve by the substitution method. x-y=-1 7x+3y=-67 what is the solution set?       Log On


   

Question 583100: solve the following system bu substitution
x=7y+9
x=7/4y
what is the solution set?

solve by the substitution method.
x-y=-1
7x+3y=-67
what is the solution set?

solve by the elimination method.
2x-5y=36
5x+7y=-27
what is the solution set?

use the elimination method to solve the system of equations.
5x+4y=5
-7x-8y=-19
what is the solution set?
Found 2 solutions by solver91311, JBarnum:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


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Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Ill do one substitution and one elimination that way you can see the difference you should be able to get the other 2 just fine
7%2F4y=7y%2B9
7=28y%5E2%2B36y
0=28y%5E2%2B36y-7
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 28y%5E2%2B36y%2B-7+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2836%29%5E2-4%2A28%2A-7=2080.

Discriminant d=2080 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-36%2B-sqrt%28+2080+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%2836%29%2Bsqrt%28+2080+%29%29%2F2%5C28+=+0.171553875070813
y%5B2%5D+=+%28-%2836%29-sqrt%28+2080+%29%29%2F2%5C28+=+-1.4572681607851

Quadratic expression 28y%5E2%2B36y%2B-7 can be factored:
28y%5E2%2B36y%2B-7+=+28%28y-0.171553875070813%29%2A%28y--1.4572681607851%29
Again, the answer is: 0.171553875070813, -1.4572681607851. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+28%2Ax%5E2%2B36%2Ax%2B-7+%29

y=.1716
y=-1.4573
x=7y%2B9
x=10.2012
x=-1.2011
_______________
2x-5y=36
5x+7y=-27
im going to eliminate the ys
multiply top equation by 7 and bottom by 5
7%282x-5y%29=7%2836%29
5%285x%2B7y%29=5%28-27%29
.
14x-35y=252
25x%2B35y=-135 add the equations together
.
14x%2B25x-35y%2B35y=252-135 add like terms
.
39x=117 divide by 39
.
highlight%28x=3%29
.
2x-5y=36 imput x value and solve for y
2%283%29-5y=36
6-5y=36
-5y=30
highlight%28y=-6%29