1. Give an example of a system of two equations with two variables that has infi
ID: 3116224 • Letter: 1
Question
1. Give an example of a system of two equations with two variables that has infinitely many solutions.
2. Change one number in your system of equations from part 1 to make it a system that has no solutions.
3. Solve the two systems to verify they have the correct outcomes.
Hint: A system of equations with two variables that has infinitely many solutions is one where the two equations turn out to be the exact same line. That is, if you graphed the two lines, you would see that they have the same slope and the same y-intercepts. In order for that to happen, one equation has to be dependent on the other... or one equation is the same as the other equation except it is multiplied on both sides by some number....
If you graphed a system of equations that has no solutions, you would find that they are parallel lines. That is, they would have the same slope but different y-intercepts. The number that you would have to change should be the number that ends up being the y-intercept.
Explanation / Answer
a system of two equations which has infinitely many solutons are
2x + 5y = 6
4x + 10y = 12
now changing one number to make the equations for no solution
first equation if becomes
2x+ 5y = 21
and second equation remains same that is 4x + 10y = 12
then this system will have no solution
solving 1st system
multiplying equaton 1 by -2 and adding equation 2 to it
-2(2x + 5y = 6)
-4x -10y = -12
4x + 10y = 12
----------------------
0 =0
since left side = right side
hence , this equations has infinite solution
now solving other set of equations
multiplying equation 1 by -2 and adding equation 2 to it
-2(2x+ 5y = 21)
-4x - 10y = - 42
4x + 10y = 12
---------------------
0 = 30
since left side is not equal to right side
hence , equations have no solutions
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