Question 16·Easy·Systems of Two Linear Equations in Two Variables
The ordered pair satisfies the system shown. What is the value of ?
For systems of equations where one equation already solves for a variable (like ), quickly use substitution: plug that value into the other equation to create a simple one-variable equation. Then isolate the remaining variable using basic inverse operations (addition/subtraction first, then multiplication/division). This avoids unnecessary graphing or elimination steps and is usually the fastest and least error-prone approach on the SAT.
Hints
Start with the easier equation
Look at the first equation. Can you immediately tell what equals?
Substitute the known value
Once you know , replace in the second equation with that value. What equation in terms of do you get?
Solve the one-variable equation
You should now have an equation like . How can you isolate using inverse operations?
Desmos Guide
Graph the first equation
In Desmos, type x = 7 to graph the vertical line that represents the first equation.
Graph the second equation
In a new line, type x = y + 3 (or equivalently y = x - 3) to graph the second line.
Find the intersection point
Click or tap on the point where the two lines intersect. Desmos will show the coordinates of this point .
Read the value of
Look at the -coordinate of the intersection point. That -value is the solution to the system and answers the question.
Step-by-step Explanation
Use the first equation
From the first equation, , so we know the exact value of .
Substitute into the second equation
Take and plug it into the second equation .
This gives the equation
Isolate in the equation
To solve for , you need to get alone. Subtract from both sides of the equation:
Compute the final value of
Evaluate to get , so .
Therefore, the value of is .