Question 100·Easy·Systems of Two Linear Equations in Two Variables
Consider the system of equations below. What is the solution ?
On SAT system-of-equation questions with nicely aligned coefficients, use elimination: add or subtract the equations to remove one variable, solve the resulting one-variable equation, then substitute back to find the other variable. For multiple-choice questions, you can also plug each option into both equations, but elimination is usually faster and avoids extra arithmetic, especially when one variable’s coefficients are opposites, as in this problem.
Hints
Think about eliminating a variable
Look at the coefficients of in the two equations: one is and the other is . What happens to if you add the equations together?
Reduce to one variable
After you add the two equations, you should get an equation with only . Solve that equation to find the value of .
Use substitution to finish
Once you know , plug it back into either or to find , then match your pair to one of the answer choices.
Desmos Guide
Enter each equation as a line
In separate lines in Desmos, type the equations solved for :
y = 9 - xy = 2x - 3
Find the intersection point
Look at the graph and identify the point where the two lines cross. The coordinates of that intersection give the solution to the system; match that ordered pair to the correct answer choice.
Step-by-step Explanation
Choose a method to solve the system
We want a single pair that satisfies both
The coefficients of are and , so adding the equations will eliminate quickly. This is called the elimination method.
Eliminate and solve for
Add the left sides and right sides of the two equations:
Now solve for by dividing both sides by :
Find and identify the solution pair
Substitute into one of the original equations, for example :
So the solution to the system is , which corresponds to choice C.