Question 139·Easy·Systems of Two Linear Equations in Two Variables
A system of two linear equations is shown.
What is the solution to the system?
For systems of two linear equations, look for the quickest way to eliminate a variable: if coefficients line up nicely (like and ), you can add the equations to eliminate that variable in one step; otherwise, use substitution by isolating the easier variable in one equation and plugging into the other. Always solve for one variable, back-substitute to find the other, and then quickly check your pair in both equations before choosing the matching answer.
Hints
Use the simpler equation first
Look at . Which variable is easier to isolate from this equation, or ?
Substitute into the other equation
Once you solve the first equation for one variable, replace that variable in the second equation with the expression you found.
Check your solution in both equations
After finding values for and , plug them into both original equations to be sure they work in each one.
Desmos Guide
Enter both equations as lines
Type y = 8 - x into one line and y = 2x - 1 into another line in Desmos so both graphs appear.
Find the intersection point
Zoom or move the graph as needed and tap/click on the point where the two lines intersect; Desmos will display the coordinates of that intersection.
Interpret the intersection
Use the -coordinate and -coordinate of the intersection point as the solution to the system, and match that ordered pair to one of the answer choices.
Step-by-step Explanation
Isolate one variable from the first equation
Start with the first equation:
Solve for :
Now you have written in terms of .
Substitute into the second equation and simplify
Take the expression for and substitute it into the second equation :
Distribute the minus sign and combine like terms:
Now you have an equation with only .
Solve for both variables and write the ordered pair
Solve :
Use to find :
So the solution to the system, written as , is .