Activity
Solve each system of equations without graphing, show your reasoning, and check your solutions.
System A
Use System A to answer questions 1 – 3.
What is the value of ?
-1
What is the value of ?
3
Show your reasoning and check the solution.
Compare your answer:
System B
Use System B to answer questions 4 – 6.
What is the value of ?
2
What is the value of ?
1
Show your reasoning and check the solution.
Compare your answer:
System C
Use System C to answer questions 7 – 9.
What is the value of ?
-3.5
What is the value of ?
4
Show your reasoning and check the solution.
Compare your answer:
System D
Use System D to answer questions 10 – 12.
What is the value of ?
5
What is the value of ?
2
Show your reasoning and check the solution.
Compare your answer:
Are you ready for more?
Extending Your Thinking
This system has three equations:
Add the first two equations to get a new equation.
Compare your answer:
Add the second two equations to get a new equation.
Compare your answer:
Solve the system of your two new equations, then answer questions 3 and 4.
What is the value of ?
Compare your answer:
-3
What is the value of ?
Compare your answer:
14
Solve the original system of equations, then answer questions 5 – 7.
What is the value of ?
Compare your answer:
9
What is the value of ?
Compare your answer:
-3
What is the value of ?
Compare your answer:
14
Self Check
Additonal Resources
Solving a System of Equations by Elimination
Let’s reinforce the steps to solve a system of equations using elimination.
Step 1 - Write both equations in standard form. If any coefficients are fractions, clear them.
Step 2 - Check to see if the coefficients of one variable are opposites or equivalent.
Step 3 - Add or subtract the equations to eliminate one variable.
Step 4 - Solve for the remaining variable.
Step 5 - Substitute the solution from Step 4 into one of the original equations. Then solve for the other variable.
Step 6 - Write the solution as an ordered pair.
Step 7 - Check that the ordered pair is a solution to both original equations.
Example
Let’s look at an example. Solve the following system of equations using elimination:
Step 1 - Write both equations in standard form. If any coefficients are fractions, clear them.
Step 2 - Check to see if the coefficients of one variable are opposites or equivalent. The coefficients on the -variables are opposites. We can add the equations.
Step 3 - Add the equations to eliminate one variable.
Step 4 - Solve for the remaining variable.
Step 5 - Substitute the solution from Step 4 into one of the original equations. Then solve for the other variable. \begin{array}{rcl}3x-3y&=&-24\\3x-3(3)&=&-24\\3x-9&=&-24\\3x&=&-15\\x&=&-5\end{array}
Step 6 - Write the solution as an ordered pair.
Step 7 - Check that the ordered pair is a solution to both original equations.
Try it
Try It: Solving a System of Equations by Elimination
Solve the following system of equations using elimination:
Compare your answer:
Here is how to solve this system of equations using elimination:
Step 1 - Write both equations in standard form. If any coefficients are fractions, clear them.
Step 2 - Check to see if the coefficients of one variable are opposites or equivalent. The coefficients on the -variables are opposites. We can add the equations.
Step 3 - Add the equations to eliminate one variable.
Step 4 - Solve for the remaining variable.
Step 5 - Substitute the solution from Step 4 into one of the original equations. Then solve for the other variable.
Step 6 - Write the solution as an ordered pair.
Step 7 - Check that the ordered pair is a solution to both original equations.