To solve the pair of linear equations graphically, follow these steps:
1. Plot the First Equation:
- The first equation is [tex]\( y = -3x + 5 \)[/tex]. This equation represents a straight line with a slope of -3 and a y-intercept of 5. To plot this line:
- Start at the point (0, 5) on the y-axis, because the y-intercept is 5.
- From this point, use the slope to determine another point on the line. A slope of -3 means that for every 1 unit you move to the right on the x-axis, you move 3 units down on the y-axis. Therefore, you can plot a point at (1, 2) (since 5 − 3 = 2).
- Draw the line passing through these points.
2. Plot the Second Equation:
- The second equation is [tex]\( y = x + 2 \)[/tex]. This equation represents a straight line with a slope of 1 and a y-intercept of 2. To plot this line:
- Start at the point (0, 2) on the y-axis, because the y-intercept is 2.
- From this point, use the slope to determine another point on the line. A slope of 1 means that for every 1 unit you move to the right on the x-axis, you move 1 unit up on the y-axis. Thus, you can plot another point at (1, 3) (since 2 + 1 = 3).
- Draw the line passing through these points.
3. Find the Intersection Point:
- Once both lines are plotted, look for the point where they intersect. The coordinates of the intersection point represent the solution to the system of equations, as it is the point where both equations are satisfied simultaneously.
- In this case, the lines intersect at the point (3, 5).
Therefore, the solution to the system of equations, found graphically, is [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex]. This means the point (3, 5) lies on both lines and satisfies both equations.
