Holt Algebra 1 6-3 Solving Systems by Elimination Another method for solving systems of equations is...
12
Holt Algebra 1 6-3 Solving Systems by Elimination Another method for solving systems of equations is elimination. Like substitution, the goal of elimination is to get one equation that has only one variable. To do this by elimination, you add the two equations in the system together.
-
Upload
julianna-robbins -
Category
Documents
-
view
213 -
download
0
Transcript of Holt Algebra 1 6-3 Solving Systems by Elimination Another method for solving systems of equations is...
Holt Algebra 1
6-3 Solving Systems by Elimination
Another method for solving systems of equations is elimination. Like substitution, the goal of elimination is to get one equation that has only one variable. To do this by elimination, you add the two equations in the system together.
Holt Algebra 1
6-3 Solving Systems by Elimination
Solving Systems of Equations by Elimination
Step 1 Write the system so that like terms are aligned.
Step 2 Eliminate one of the variables and solve for the other variable.
Step 3Substitute the value of the variable into one of the original equations and solve for the other variable.
Step 4Write the answers from Steps 2 and 3 as an ordered pair, (x, y), and check.
Holt Algebra 1
6-3 Solving Systems by Elimination
Example 1: Elimination Using Addition
3x – 4y = 10x + 4y = –2
Solve by elimination.
Write the system so that like terms are aligned.
Add the equations to eliminate the y-terms.
Simplify and solve for x.
Holt Algebra 1
6-3 Solving Systems by Elimination
Example 1 Continued
Write one of the original equations.
Substitute 2 for x.
Write the solution as an ordered pair.
Holt Algebra 1
6-3 Solving Systems by Elimination
Check It Out! Example 2
y + 3x = –22y – 3x = 14
Solve by elimination.
Write the system so that like terms are aligned.
Add the equations to eliminate the x-terms.
Simplify and solve for y.
Holt Algebra 1
6-3 Solving Systems by Elimination
Check It Out! Example 2 Continued
Write one of the original equations.
Substitute 4 for y.
Write the solution as an ordered pair.
Holt Algebra 1
6-3 Solving Systems by Elimination
When two equations each contain the same term, you can subtract one equation from the other to solve the system. To subtract an equation add the opposite of each term.
Holt Algebra 1
6-3 Solving Systems by Elimination
2x + y = –52x – 5y = 13
Solve by elimination.
Example 3: Elimination Using Subtraction
Add the opposite of each term in the second equation.
–(2x – 5y = 13)
2x + y = –5
2x + y = –5–2x + 5y = –13
Eliminate the x term.Simplify and solve for y.
Holt Algebra 1
6-3 Solving Systems by Elimination
Example 3 Continued
Write one of the original equations.
Substitute –3 for y.
Simplify and solve for x.
Write the solution as an ordered pair.
Holt Algebra 1
6-3 Solving Systems by Elimination
Remember to check by substituting your answer into both original equations.
Remember!
Holt Algebra 1
6-3 Solving Systems by Elimination
Check It Out! Example 4
3x + 3y = 15–2x + 3y = –5
Solve by elimination.
Add the opposite of each term in the second equation.
Eliminate the y term.
Simplify and solve for x.
Holt Algebra 1
6-3 Solving Systems by Elimination
Check It Out! Example 4 Continued
Write one of the original equations.
Substitute 4 for x.
Simplify and solve for y.
