How do I solve the system y = 2x + 1 and y = −x + 4?
How to solve the system y = 2x + 1 and y = −x + 4: graph both lines, set them equal to get x = 1, and find the intersection point (1, 3).
Step-by-step explanation
- To solve the system of equations y = 2x + 1 and y = -x + 4, we first set up a coordinate system and plot the first line.
- Next, we plot the second line, y = -x + 4, on the same set of axes.
- The solution to the system is the point where the two lines intersect. We can find this by setting the equations equal to each other.
- Solving for x, we add x to both sides and subtract 1, giving 3x = 3, which means x = 1.
- Finally, we substitute x = 1 back into either equation to find y = 3. The intersection point is (1, 3).
This is a real answer from Math Motion AI: the explanation and the animation were made by the site for this question.
More algebra examples
- How do I solve x² − 5x + 6 = 0?
- What is the slope of the line through (1, 2) and (4, 8)?
- Solve 2x + 3 = 11 step by step.