Question 124·Easy·Systems of Two Linear Equations in Two Variables
Consider the system of equations:
The solution to the system is . What is the value of ?
(Express the answer as an integer)
When one of the equations in a system is already solved for a variable (like ), use substitution to save time: plug that expression into the other equation, solve the resulting one-variable equation, and then substitute back to find the second variable. Always check that your solution pair satisfies both original equations to avoid arithmetic mistakes.
Hints
Pick the easiest equation to work with
One of the equations already has by itself. Which one is it, and how can that help you avoid solving a more complicated system?
Use substitution
Take the expression that equals from the first equation and plug it into the in the second equation. You should get an equation with only .
Finish solving for y
After you find the value of , substitute it back into to find the corresponding value of .
Desmos Guide
Enter the equations
In Desmos, type the first equation as y = -2x + 7 on one line, and the second equation as 3x + y = 9 on another line (Desmos will graph both lines).
Locate the intersection point
On the graph, look for the point where the two lines cross. Click or tap that intersection point to see its coordinates displayed.
Read off the y-value
From the intersection point’s coordinates shown by Desmos, focus on the second number (the -coordinate). That value is the solution for in the system.
Step-by-step Explanation
Choose a method to solve the system
Notice that the first equation already has by itself:
This makes the substitution method convenient: we can substitute this expression for into the second equation.
Substitute into the second equation and solve for x
Start with the second equation:
Replace with from the first equation:
Combine like terms ():
Subtract 7 from both sides to solve for :
Substitute x back to find y
Use in the first equation :
Multiply and simplify:
So the value of in the solution is .