Question 58·Easy·Systems of Two Linear Equations in Two Variables
The system of equations is
The solution to the system is . What is the value of ?
(Express the answer as an integer)
When one equation in a system is already solved for a variable (like ), use substitution immediately: plug that value into the other equation to create a simple one-variable equation, then solve step by step (undo addition/subtraction, then multiplication/division). This is faster and less error-prone than methods like elimination for straightforward systems like this.
Hints
Notice what is already solved
Look at the second equation. One of the variables is already isolated. How can that help you?
Substitute into the other equation
Since you know the value of , replace in the first equation with that value.
Solve the resulting one-variable equation
After substitution, you will have an equation with only . Rearrange it by undoing addition/subtraction first, then multiplication/division.
Desmos Guide
Enter the equations
In Desmos, type the first equation as 2x + y = 9 on one line and the second equation as y = 3 on another line. Desmos will graph both lines.
Find the intersection
Look for the point where the two lines intersect. Click on that intersection point; Desmos will show its coordinates .
Read the x-value
From the intersection point’s coordinates, note the x-coordinate. That is the value of that solves the system.
Step-by-step Explanation
Use the given value of y
From the second equation, we know .
Substitute into the first equation to get:
Solve the equation for x
Now solve :
So, the value of is .