What ordered pair satisfies the system of equations below?
For systems of two linear equations, especially when the variables have opposite coefficients (like and ), use elimination: add or subtract the equations to cancel one variable, solve for the remaining variable, then substitute back to find the other. Finally, always write the solution as an ordered pair and quickly verify it in both original equations to avoid errors from only checking one.
Hints
Think about eliminating a variable
If you add the two equations together, what happens to the terms?
Solve for one variable first
Once you combine the equations and get an equation with only , solve that equation. Then plug that value of into either original equation to find .
Check both equations
For any answer choice you consider, plug the and values into both equations and and see if they work in each.
Desmos Guide
Enter the equations as lines
In Desmos, type the first equation as y = 7 - x and the second equation as y = x - 1. Both lines will appear on the graph.
Find the intersection point
Look for the point where the two lines cross. Click or tap on that intersection point; Desmos will display its coordinates.
Use the intersection as the solution
The - and -values of that intersection point give the ordered pair that satisfies both equations in the system.
Step-by-step Explanation
Use elimination to combine the equations
You are given the system:
Add the two equations together to eliminate :
On the left side, and cancel.
Solve for x
After adding, the equation becomes
Divide both sides by to solve for :
Substitute back to find y
Now substitute into one of the original equations, for example :
Subtract from both sides:
Write and match the ordered pair
The solution to the system is the ordered pair with your -value first and your -value second, so the solution is . This matches answer choice B.