Solve the following system of equations: x + y = 2 y = -2x + 3
Understand the Problem
The question asks us to find the solution to a system of two linear equations by graphing them. The two equations are x + y = 2 and y = -2x + 3. The solution is the point where the two lines intersect on the graph.
Answer
$(1, 1)$
Answer for screen readers
$(1, 1)$
Steps to Solve
- Identify the intersection point
The graph shows two lines intersecting. We need to identify the coordinates of this intersection point.
- Read the x-coordinate
Locate the x-coordinate of the intersection point on the x-axis. From the graph, it appears to be $x = 1$.
- Read the y-coordinate
Locate the y-coordinate of the intersection point on the y-axis. From the graph, it appears to be $y = 1$.
- Write the solution as a coordinate pair
The solution to the system of equations is the point $(1, 1)$.
$(1, 1)$
More Information
The solution to the system of equations is the point where both equations are true. Substituting $x = 1$ and $y = 1$ into both equations confirms this: Equation 1: $1 + 1 = 2$ Equation 2: $1 = -2(1) + 3 = -2 + 3 = 1$
Tips
A common mistake is misreading the graph, especially if the intersection point is not exactly on a grid line. Carefully tracing from the intersection to both axes is crucial. Another mistake is confusing the x and y coordinates, writing (y, x) instead of (x, y).
AI-generated content may contain errors. Please verify critical information
