Question 106·Easy·Systems of Two Linear Equations in Two Variables
The system of equations is
What is the solution to the system of equations?
When a system of equations includes one equation already solved for a variable (like ), immediately use substitution: plug that value into the other equation, solve for the remaining variable, then form the ordered pair . On multiple-choice SAT questions, you can also quickly check by plugging each option into both equations and seeing which one satisfies both, but substitution is usually faster and less error-prone here.
Hints
Start with the simpler equation
One of the equations already tells you the value of . Use that first.
Substitute into the other equation
Take the value of from the second equation and plug it into the first equation .
Solve step by step
After substituting, simplify the multiplication, then isolate . Finally, pair the -value with the -value from the second equation.
Desmos Guide
Enter the first equation
In Desmos, type y = (25 - x)/5 to represent the equation solved for .
Enter the second equation
On a new line, type y = 3 to graph the horizontal line from the second equation.
Find the intersection point
Look for the point where the two graphs intersect; read off the - and -coordinates of that intersection. That ordered pair is the solution to the system.
Step-by-step Explanation
Use the equation that is already solved for a variable
From the system,
y is already given as in the second equation. We will use this value in the first equation.
Substitute into the first equation
Replace with in the first equation :
Now simplify and solve for .
Solve for and write the ordered pair
Compute , so the equation becomes
Subtract 15 from both sides:
We already know , so the solution to the system is the ordered pair .