A Point of Intersection - University of Nebraska Omaha
A Point of Intersection
Student Worksheet
Directions: Solve each system of equation by graphing. Estimate the solution. Then, verify your solution by solving using a different method (substitution or elimination).
Let’s look at an example first.
|y = x |Estimated Solution |Verify Solution |
|y = -x + 2 | | |
| | |Substitution Method |
|[pic] | | |
| | |x = -x + 2 |
| |(1, 1) |+ x +x |
| | |2x = 2 |
| | |2 2 |
| | | |
| | |x = 1 |
| | | |
| | |y = x |
| | |1 = 1 |
| | |[pic] |
| | | |
| | |y = -x + 2 |
| | |1 = -1 + 2 |
| | |1 = 1 |
| | |[pic] |
Remember: If the lines don’t cross at a point of two integers, it’s OK to estimate. Then, when you verify the solution, you will find the exact point.
|y = 2x + 2 |Estimated Solution |Verify Solution |
|y = -x + 1 | | |
|[pic] | | |
|y = 2x + 1 |Estimated Solution |Verify Solution |
|y = x + 1 | | |
|[pic] | | |
Now it’s your turn! Create 2 linear equations by filling in each blank with the following numbers: -2, -1 1 2. Graph the lines on the coordinate plane. Estimate the solution. Then verify the solution by solving the system using a different method (substitution or elimination).
|Linear Equation 1 |Estimated Solution |Verify Solution |
| | | |
|y = ____x + ____ | | |
| | | |
|Linear Equation 2 | | |
| | | |
|y = ____x + ____ | | |
| | | |
| | | |
|[pic] | | |
| | | |
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