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Solving Simultaneous Equations by Graphing: x + 2y = 2 and 2x + 2y = 5
Published on April 16, 2026
Algebra
Learn how to solve a system of linear equations by graphing the two lines and finding their intersection point.
Question
Answer
Hereโs how to solve the system of equations by plotting:
1. Rewrite the equations in slope-intercept form (
-
Equation 1:
- Subtract
from both sides: - Divide both sides by 2:
- Subtract
-
Equation 2:
- Subtract
from both sides: - Divide both sides by 2:
- Subtract
2. Plot the lines on the graph:
-
Line 1 (
): - The y-intercept is 1. Plot a point at (0, 1).
- The slope is
. From the y-intercept, go down 1 unit and right 2 units. Plot another point at (2, 0). - Draw a line through these two points.
-
Line 2 (
): - The y-intercept is
or 2.5. Plot a point at (0, 2.5). - The slope is -1. From the y-intercept, go down 1 unit and right 1 unit. Plot another point at (1, 1.5).
- Draw a line through these two points.
- The y-intercept is
3. Find the intersection point:
The solution to the system of equations is the point where the two lines intersect on the graph. Observe the graph to find this point.
Solving algebraically to verify:
We can also solve this system algebraically to find the exact intersection point.
Subtract Equation 1 from Equation 2:
Now substitute the value of
Answer:
The intersection point, and therefore the solution to the simultaneous equations, is