Solve each of the following systems of equations graphically by (1) finding the slope-intercept forms and (2) graphing:

As seen by the intersection in Fig. 4-6, the solution is x = 2, y = −1.

As seen in Fig. 4-7, the solution is x = 4, y = 2.

As seen in Fig. 4-12, there is an infinite number of solutions and no unique solution because the two equations are equivalent or dependent. In terms of Sections 4.2, m1 = m2 and b1 = b2. With the two equations equivalent, there is, in effect, only one independent equation and the system is underconstrained. An underconstrained system has multiple solutions or no solution, never a unique solution.

As seen in Fig. 4-13, there is no unique solution because there is no one point at which all the graphs intersect simultaneously. An overconstrained system in which n > ν seldom has a unique solution.

Transcribed Image Text:

(a) 12x + 3y = 21 -2x+4y-8 (1) Finding the slope-intercept forms by solving each equation for y in terms of x, (2) See Fig. 4-6. 12x + 3y = 21 -2x+4y == -8 y = -4x+7 y = x -2