annapitch.blogg.se

If a system has a unique solution (one point of intersection), the system is consistent.

The term simultaneous is frequently used to emphasize the idea that the solution of a system is the point that satisfies both equations at the same time, or simultaneously. When two linear equations are considered together, they are called a system of linear equations, or a set of simultaneous equations. These three examples constitute all three possible situations involving the graphs of two linear equations. Any point that satisfies one equation will also satisfy the other This can be seen easily by putting both equations in the slope-intercept form :īoth equations are identical when written in the same form. The lines not only intersect they are the same line. The reason there is just one Line is that both equations represent the In this case, we could have anticipated the result by writing both equations in the intercept form and noted that both lines have the same slope, -1:ĭo the lines y=-x+4 and 2y + 2x = 8 intersect? If so, where do they intersect? If not, why not? The graphs of both lines are shown in Figure 9.3. The lines do not intersect because they are parallel. This intersection can be checked by substituting x = 1 and y = 3 into both equations:ĭo the lines y = -x + 4 and x + y = 2 intersect? If so, where do they intersect? If not, why not? The answers are in the graphs in Figure 9.2. The lines appear to intersect at the point (1, 3), or where x = 1 and y = 3. What do you think they are’? Stop to think about your lines and those of the other people in class before you read further.ĭo the lines y = -x + 4 and y = 2x + 1 intersect (cross each other)? If so, where do they intersect? If not, why not? We can answer these questions by graphing both equations as in Figure 9.1. What two lines did you see‘? No matter what specific lines you envisioned, there are only three basic positions for the lines relative to each other. Visualize two straight lines on the same graph.