Section 3.5 Intersecting Lines © Copyright all rights reserved to Homework depot: www.BCMath.ca

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

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

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

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

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!!

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

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

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

Amc12b 2007