Systems of equations can have: one solution , no solution , or infinitely manyso
ID: 3095717 • Letter: S
Question
Systems of equations can have: one solution,no solution, or infinitely manysolutions.Describe how the end result of a system of equations would look foreach of the situations (no need to solve the entire system, justrepresent the end result). Describe how the solutions of theequations would look on a graph as well.
One solution solved algebraically:
One solution graphed:
No solution solved algebraically:
No solution graphed:
Infinitely many solutions solved algebraically:
Infinitely many solutions graphed:
Explanation / Answer
One solution: algebraically -3x + y = 2 3x + y = -5 add the two equations to get 0x + 2y = 3 2y = 3 y = 3/2 -3x+(3/2)=2 -3x = 1/2 x=-1/6 Graphed: two lines intersect at one point No solution: algebraically -3x + y = 2 -3x + y = -5 multiply eq1 by -1 and add to eq2 0+0 = -7 so obviously 0 is not equal to -7 Graphed: two parallel lines (so there is no intersection point) Infinitely many solutions algebraically: x+y = 2 3x+3y = 6 multiply eq1 by -3 and add to eq 2 to get x+y = 2 0x+0y=0 graphed: the two lines are actually the same line (so they lieright on top of each other, hence every point is an intersectionpoint, hence infinite number of solutions.
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