SOLUTION: solve by substitution: {{{sqrt(x)-y=0}}} {{{2x+y=3}}}

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: solve by substitution: {{{sqrt(x)-y=0}}} {{{2x+y=3}}}      Log On


   

Question 164983: solve by substitution:
sqrt%28x%29-y=0
2x%2By=3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve by substitution:
sqrt%28x%29-y=0
2x%2By=3
-------------
sqrt%28x%29-y=0
sqrt%28x%29+=+y
square both sides
x = y^2
Sub into the 2nd eqn
2x%2By=3
2y%5E2%2By=3
2y%5E2%2By-3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B1x%2B-3+=+0) has the following solutons:

x%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=%281%29%5E2-4%2A2%2A-3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+1
x%5B2%5D+=+%28-%281%29-sqrt%28+25+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2x%5E2%2B1x%2B-3 can be factored:
2x%5E2%2B1x%2B-3+=+%28x-1%29%2A%28x--1.5%29
Again, the answer is: 1, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B1%2Ax%2B-3+%29

These are the values for y - the solver always uses x as the variable.
The solver has a problem sometimes.
It's (y-1)*(2y+3), the answers shown are correct.
So for y = 1, x = 1
For y = -3/2, x = 9/4