FILL IN THE BLANK. A system of linear equations can have​ _________________________.         A.no solution or an infinite number of solutions   B. 1 or 2 or 3 solutions   C. no solution or 1 solution   D. an infinite number of solutions   E. no​ solution, or 1​ solution, or an infinite number of solutions   F. no solution   G. 1 solution   H. 1 or 2 solutions

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Example How many solutions does each system of equations have? b. y = 7x + 3 y = 7x a. The lines intersect at one point. There is exactly one solution. b. y cannot equal both 7x + 3 and 7x at the same time. There is no solution. What does the graph show to be the solution of the system in part a of the Example? one soluti Find a value for m that will give you a system of equations with exactly one solution. 3 Find a value for b that will give you a system of equations with no solution. Draw a line in each coordinate plane so that the lines represent a system of equations with the given number of solutions. a. no solution -2 b. exactly one solution c. infinitely many solutions 2 y = 6x + 1 y = mx + 1 -20 y = 6x + 1 y = 6x + b -2

Name 23 Date A.2(1) write systems of two linear equations given a table of values, a graph, and a verbal description. 1. Braeden sold t-shirts and caps for the school cross-country fundraiser. The t-shirts, t, sold for $20 each and the caps, c, sold for $15 each. Braeden sold a total of 96 t-shirts and caps earning a total of $1,665. Which system of equations best represents this situation? C 20t + 15c = 1,665 At +c = 1,665 20t + 15c = 96 20t + 15c = 96 Dt +c = 96 Bt = 96 + c 15t + 20c = 1,665 20t + 15c = 1,665 2. A system of equations is graphed below. y -4- -2-