SOLUTION: Write a system of two linear equations that has . a) only one solution ,(5,1). b) an infinite number of solutions . c) no solution.

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Question 504909: Write a system of two linear equations that has .
a) only one solution ,(5,1).
b) an infinite number of solutions .
c) no solution.
Answer by emargo19(101) About Me  (Show Source):
You can put this solution on YOUR website!
a) only one solution ,(5,1) ****instead of (2,3)
Lets use point slope intercept equation
let's say the slope is -2.
So,
%28y-y1%29=m%28x-x1%29+
%28y-1%29=-2%28x-5%29
y-1=-2x%2B10
y=-2x%2B11----Eq1

For next equation:
Lets use point slope intercept equation
let's say the slope is 2.

y-y1=m%28x-x1%29
y-1=2%28x-10%29
y=2x-9 ----Eq2

Next lets check

Lets substitute
y=2x-9 in eq 1
y=-2x%2B11
So,
2x-9=-2x%2B11
4x=11%2B9
4x=20
x=5
Next lets substitute x=5 in eq
y=2%285%29-9
y=10-9
y=1

Therefore eqs are
y=-2x%2B11----Eq1
y=2x-9 ----Eq2

----------------------
For NO SOLUTION
REmember:
No solution happens when two graphs are parallel. It looks like this (0=7)
To make lines Paralel we have to have equal slopes.
Lets use the point slope equation
Lets choose points (3,2) and slope as 4.
y-y1=m%28x-x1%29
y-3=4%28x-2%29
y=4x-8%2B3
y=4x-5 ----eq1

Lets use the point slope equation again
This time lets choose points (2,1) and slope as 4.
y-y1=m%28x-x1%29
y-1=m%28x-2%29
y=4x-8%2B1
y=4x-7 ----eq2
Lets check:
y=4x-5
y=4x-7
Substitute y=4x-7 in eq y=4x-5
4x-7=4x-5
4x-4x=-5%2B7
0=2

c)infinite number of solutions
All that you need to do here is to write an equation and make a second equation a multiple
of the first equation. Example:
.
The first equation is y = 2x +1 ---eq1
.
The second equation is 2y = 4x + 2 ---eq2
.
This 2nd equ is just 2 times the 1st eq.
So this makes both eq the same they will have the same graph(1 line on the graph. So, these two eqns will have an infinite number of common
solns.