Without graphing, answer the questions for the following linear system. yx=3 x+y

Question

Without graphing, answer the questions for the following linear system. yx=3 x+y=8 (a) Is the system inconsistent, or are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? (a) Is the system inconsistent, or are the equations dependent, or neither? Inconsistent system Dependent equations Neither (b) Describe the graph. Parallel lines One line Intersecting lines (c) Determine the number of solutions. One solution Infinite solutions No solution Click to select your answer.

Explanation / Answer

y-x=-3 or y=x-3

y+x=8

put the value of y from eqn1 into eqn2

x-3+x=8 or 2x=11 or x=11/2

y=11/2 -3=5/2

this means x and y have finite and unique value solution

a) system is consistent or an unique number of solutions.

b) the graph a pair of intersecting lines

c) system have one solution

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