Question 55·Easy·Systems of Two Linear Equations in Two Variables
Consider the system of equations:
What is the value of ?
For systems of two linear equations on the SAT, quickly check if adding or subtracting the equations will eliminate a variable (as it does here with ). Use elimination to solve for one variable, then substitute that value back into either original equation to find the other variable. Finally, confirm your result by mentally checking it in both equations and make sure you are giving the variable the question asks for (here, , not ).
Hints
Think about combining the equations
Look at the two equations and notice that one has and the other has . What happens to if you add the two equations together?
Solve for one variable first
After you combine the equations so that disappears, you will get an equation with only . Solve that equation for .
Plug back in to find
Once you know , substitute it into one of the original equations (for example, ) to solve for , then look for that number in the answer choices.
Desmos Guide
Enter the first equation in Desmos
Rewrite the first equation as and type y = 6 - x into Desmos.
Enter the second equation in Desmos
Rewrite the second equation as and type y = 3x - 10 into Desmos.
Find the intersection point
Look at the point where the two lines intersect. The -coordinate of this intersection point is the value of that solves the system.
Step-by-step Explanation
Use elimination to remove one variable
Notice that the system is:
If you add the two equations together, the and terms cancel out:
This simplifies to an equation in terms of only.
Solve for
Combine like terms:
so
Divide both sides by 4:
Substitute to find and match the answer choice
Use in one of the original equations. Using :
Subtract 4 from both sides:
So the value of is , which corresponds to answer choice B.