Y=-x+6 y=3x-2. Estimate the solution to the system of these linear equations based on the graph y=-x+6 y=3x-2
To estimate the solution to the system of linear equations based on the given graphs, we need to find the point where the two lines intersect. Let's break down the process step by step:
1. Start by plotting the two equations on a graph:
- Equation 1: y = -x + 6
- Equation 2: y = 3x - 2
2. To plot the first equation, start at the y-intercept, which is 6, and then use the slope (-1) to find additional points. Since the slope is negative, move one unit right and one unit down to get the next point. Connect all the points to draw the line.
3. To plot the second equation, start at the y-intercept, which is -2, and then use the slope (3) to find additional points. Since the slope is positive, move one unit right and three units up to get the next point. Connect all the points to draw the line.
4. The estimate for the solution to the system of equations is the point where the two lines intersect. Locate this point by visually observing the graph.
It's important to note that estimating the solution from a graph can introduce some level of inaccuracy. For a more precise solution, we can solve the system of equations algebraically.