Intermediate Algebra Multiple-Choice Practice Guidance

Q1. A system of equations has been graphed to the right. Find the solution to the system as an ordered pair (x, y).

Background

Topic: Systems of Linear Equations (Graphical Solution)

This question tests your ability to interpret the solution of a system of two linear equations by identifying the intersection point of their graphs.

Key Terms and Concepts:

• System of equations: Two or more equations with the same variables.

• Solution to the system: The point(s) (x, y) that satisfy both equations simultaneously. Graphically, this is where the lines intersect.

Step-by-Step Guidance

1. Look at the graph and identify where the two lines (one red, one blue) intersect. This point is the solution to the system.

2. Read the coordinates of the intersection point carefully. Make sure to count the grid lines accurately for both x and y values.

3. Check the possible answer choices and match the coordinates you found to one of the options.

4. Remember, if the lines are parallel and never intersect, the system has no solution. If the lines overlap completely, there are infinitely many solutions.

Try solving on your own before revealing the answer!

Final Answer: (3, 4)

The intersection point of the two lines is at (3, 4). This is the only point that satisfies both equations, so it is the solution to the system.