Question 23·Medium·Systems of Two Linear Equations in Two Variables
The ordered pair satisfies the system of equations above. What is the value of ?
For systems of two linear equations, quickly check if one variable has coefficients that are opposites (like and ). If so, use elimination by adding the equations to cancel that variable, solve the resulting one-variable equation, and only substitute back if you also need the other variable. This keeps the algebra short and reduces chances for errors.
Hints
Look at the y-coefficients
Compare the coefficients of in the two equations. How are and related?
Combine the equations
Try adding the two equations together. What happens to the -terms when you do this?
Solve the simpler equation
After adding, you should have an equation with only . How do you isolate in that equation?
Desmos Guide
Enter the two equations
In the first expression line, type 2x+3y=18. In the second line, type 4x-3y=6. Desmos will graph both lines.
Find the intersection point
Click or tap where the two lines intersect. Desmos will display the coordinates of this intersection point .
Read the x-value
Look at the x-coordinate of the intersection point; that value is the solution for in the system.
Step-by-step Explanation
Eliminate one variable by adding the equations
Notice the -terms are and . If we add the two equations, the -terms will cancel:
On the left side, and cancel out, and combine:
Now we have an equation with only .
Solve the resulting equation for x
From the equation , divide both sides by :
So, the value of is , which corresponds to choice C.