The lesson

This lesson teaches Systems by Graphing. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Graph both lines

When you study graph both lines, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

1Write each equation in slope-intercept form if needed.
2Graph both lines on the same grid.
3The intersection point is the solution.

Where do y = x + 1 and y = -x + 3 intersect?

1Graph both lines.
2They cross at (1, 2).
3Check: 1 + 1 = 2 ✓ and -1 + 3 = 2 ✓.

Why this matters

Systems by Graphing shows up constantly in the solution is the point where the two lines cross. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

Graph both lines
Write each equation in slope-intercept form if needed.
Graph both lines on the same grid.
The intersection point is the solution.

Video walkthrough

Other

Solving a System by Graphing

Graph both lines and read the intersection point.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Solve by graphing: y = x and y = 2. What is the solution?