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Class Notes for Lecture Day 18
Systems of Equations
Solving Linear Systems, Method 2: Substitution
For each of the following equations, substitute the given value and solve.
3x + 2y = 8; x = 4
5x – 3y = 12; y = 3x
2x + 6y = 10; y = 2x - 3
The Substitution Method:
1. Solve one of the equations for one of the variables.
2. Substitute the result into the other equation.
3. Solve for the remaining variable.
If the variable is eliminated giving a true statement, the system is dependent.
If the variable is eliminated giving a false statement, the system is inconsistent.
4. Substitute the result into the equation found in step 1 and solve.
5. Write your solutions for x and y as an ordered pair.
Solve each of the following systems using the Substitution Method.
Solving Linear Systems, Method 3: Elimination
Add the following pairs of equations:
3x + 5 = 6
6x – 5y = 10
-2x – 5 = 1
3x + 5y = 27
8x + 2y = 13
-7x – 6y = 12
2(x + 3y) = (4)2
-3(-x + 2y) = (5)(-3)
The Elimination Method:
1. Express each equation in the form Ax + By = C.
2. Multiply both sides of one (or both) of the equations by a nonzero number so
that the coefficients of either x or y in the two equations are opposites.
3. Add the equations.
If the variable is eliminated giving a true statement, the system is dependent.
If the variable is eliminated giving a false statement, the system is inconsistent.
4. Solve for the remaining variable.
5. Substitute the solution into one of the original equations and solve for the
other variable.
6. Write the solutions of x and y as an ordered pair.
Solve each of the following systems using the Elimination Method: