1. Section 3.5 Intersecting Lines
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2. Finding the Intersecting Point:
There are two ways to find the intersection point
Solving by Elimination:
Find the LCM for the coefficients for ‘x’
Multiply each equation so that the coefficients of ‘x’ are equal
Add/subtract the equations to cancel out one variable
Solve
Plug the answer back into the original equation and solve for the 2nd variable
Solving by Substitution:
isolate a variable from one equation
Then “substitute” that variable into the 2nd equation

3. Ex: Solve the system by Addition/Subtraction
1. Coefficients of “x”
2. LCM: 12
3. Subtract the equations
4. Solve for the remaining variable
5. Plug into original equation to solve for 2nd variable

4. Practice: Solve By Addition/Subtraction
Multiply all terms by LCD to cancel out your denominators
Coefficients of “x”
Add the equations

5. Properties of Linear Systems:
Multiplying an entire equation by a constant does not change the solution
Adding or subtracting two equations does not change the solution
Slope and Y-intercept
are still the same

6. Adding/Subtracting the equations will give you the Same solution!!x y -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
Add the Equations
Subtract the Equations
Adding/Subtracting the equations will give you the
Same solution!!

7. Isolate “y” variable from
Substitute equation into
Solve
Solve for “y” using
Therefore, the solution is:

8. Practice: Solve by Substitution
Isolate “y” variable from
Substitute equation into
Solve
Solve For “y” with:

10. Ex: Three lines are drawn and the intersection points are used to make a triangle. What is the area of the triangle?

11. Amc12b 2007