Question 70·Easy·Systems of Two Linear Equations in Two Variables
What is the solution to the system of equations above?
For systems where one equation is already solved for a variable (like ), immediately use substitution: plug that value into the other equation, solve for the remaining variable, then write the solution as an ordered pair. On multiple-choice questions, you can also quickly check options by substituting the and values into both equations and seeing which pair makes both equations true, but substitution is usually faster and less error-prone for simple systems like this.
Hints
Start with the easier equation
One of the equations already gives you the value of a variable directly. Use that equation first.
Substitute into the other equation
After you know , replace in the first equation with that value and write the new equation involving only .
Check which ordered pair fits both equations
Once you find , pair it with the value you already know and make sure this ordered pair makes both original equations true.
Desmos Guide
Graph both equations
In Desmos, type 2x + y = 13 on one line and y = 7 on another line to graph both lines.
Find the intersection point
Look for the point where the horizontal line meets the slanted line . Note 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,
notice that the second equation already tells you the value of : .
Substitute into the other equation
Replace with in the first equation .
This gives
Solve for
Solve the equation :
Write the solution as an ordered pair
You found and . So the solution that makes both equations true is the ordered pair .