Question 85·Easy·Systems of Two Linear Equations in Two Variables
The system of equations is
If is the solution to the system, what is the value of ?
For systems of two linear equations on the SAT, elimination is often the fastest: line up the equations, look for a variable that can be cancelled by adding or subtracting the equations, then solve the resulting one-variable equation. Keep arithmetic clean—especially when adding constants and dividing—then, if needed, quickly check your solution by plugging back into one original equation.
Hints
Think about eliminating a variable
Look at how appears in both equations. Is there a way to combine the equations so that the terms cancel out?
Try adding the equations
What happens if you add the left sides together and the right sides together: and ?
Solve the resulting equation
After combining the equations, you will get an equation with only . Solve that equation to find .
Desmos Guide
Enter both equations in Desmos
In one line, type y = 11 - 2x (this is the same as ). In another line, type y = x - 1 (this is the same as ).
Find the intersection point
Look for the point where the two lines intersect. Click on the intersection if needed; Desmos will show its coordinates . The value of in that ordered pair is the answer to the question.
Step-by-step Explanation
Write the system clearly
We are given the system of equations:
We want to find the value of that makes both equations true at the same time.
Use elimination to remove one variable
Notice that the first equation has and the second equation has .
If we add the two equations together, the terms will cancel:
On the left side, and cancel, and the terms combine. On the right side, the constants add.
Simplify the combined equation and solve for x
Simplify the result of adding the equations:
Now solve this equation for by dividing both sides by :
So, the value of in the solution is , which corresponds to answer choice C.