• The solutions to a system of equations are the points of intersection of the graphs.
• For a system consisting of a linear equation and a quadratic equation:
linear equation: y=mx+b
quadratic equation: y=ax2+bx+c
There are 3 cases to consider:
case 1: 2 solutions
case 2: 1 solution
case 3: no solutions
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Examples
Lessons
Case 1: System with 2 Solutions
Solve the system: y=−x+1 y=x2+x−2
Verify the solutions graphically
Case 2: System with 1 Solution
Solve the system: 2x−y=8 y=x2−4x+1
Verify the solutions graphically
Case 3: System with No Solutions
Solve the system: 10x+5y+15=0 y=x2−4x+2
Verify the solutions graphically
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The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.