SOLUTION: Can you please explain to me about what is a one solution, and no solution infinitive solution mean in a simple way? I am more of visual in number than word explanation. How do

Question 44801: Can you please explain to me about what is a one solution, and no solution infinitive solution mean in a simple way? I am more of visual in number than word explanation. How do you know what they are when you solve the equation? Do you sitll have to process the equation with y=mx+b when you have equation x+2y=10 and 4y-20=2x
How do you solve by graphing? and what is the solution?
Your help is greatly appericated.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Can you please explain to me about what is a one solution, and no solution infinitive solution mean in a simple way? I am more of visual in number than word explanation.
If you graph two lines and find that they cross at one point the system of
equations has one solution.
If the two lines are parallel and do not cross at any point the system has
no solutions.
If the two lines lie on top of one another the system has an infinite number
of solutions.
-------------------------------------------------------------
How do you know what they are when you solve the equation? Do you sitll have to process the equation with y=mx+b when you have equation x+2y=10 and 4y-20=2x
The "system of equations" may be solved in many ways: graphing, substitution,
elimination, matrices, etc.
------------------------------------------
How do you solve by graphing? and what is the solution?
You graph lines by finding two points on the line, plotting the points on
a coordinate system, and drawiing a line through the points. The solution
is a pair of numbers that make the equation a true statement.
--------------------------------------------
x+2y=10 and 4y-20=2x
To solve this system by substitution proceed as follows:
Solve the 1st equation for "x".
x=10-2y
Substitute that value into the 2nd equation, as follows:
4y-20=2(10-2y)
Simplify, as follows:
4y-20=20-4y
8y=40
y=5
Substitute that value into one of the equations to find a value for "x".
x=10-2(5)=0
So the solution is (0,5)
Check that answer in the other equation, as follows:
4y-20=2x
4(5)-20=2(0)
20-20=0
0=0
The solution checks.
These two lines meet at one point; the point is (0,5).
Cheers,
Stan H.

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