Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. EXAMPLE 3 Identify the number.

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Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. EXAMPLE 3 Identify the number of solutions a. 5x + y = –2 Equation 1 –10x – 2y = 4 Equation 2 SOLUTION y = –5x – 2 Write Equation 1 in slope- intercept form. y = –5x – 2 Write Equation 2 in slope- intercept form. ANSWER Because the lines have the same slope and the same y -intercept, the system has infinitely many solutions.

EXAMPLE 3 Identify the number of solutions. SOLUTION Write Equation 1 in slope-intercept form. Write Equation 2 in slope-intercept form. ANSWER Because the lines have the same slope but different y - intercepts, the system has no solution. b. 6x + 2y = 3 Equation 1 6x + 2y = –5 Equation 2 b. y = –3x y = –3x – 5 2

EXAMPLE 4 Write and solve a system of linear equations ART An artist wants to sell prints of her paintings. She orders a set of prints for each of two of her paintings. Each set contains regular prints and glossy prints, as shown in the table. Find the cost of one glossy print. RegularGlossyCost 4530$ $155

EXAMPLE 4 Write and solve a system of linear equations SOLUTION STEP 1 Write a linear system. Let x be the cost ( in dollars ) of a regular print, and let y be the cost ( in dollars ) of a glossy print. 45x + 30y = 465 Cost of prints for one painting Cost of prints for other painting 15x + 10y = 155

EXAMPLE 4 Write and solve a system of linear equations STEP 2 Solve the linear system using elimination. 45x + 30y = x + 10y = x + 30y = 465 –45x – 30y = –465 0 = 0 ANSWER There are infinitely many solutions, so you cannot determine the cost of one glossy print. You need more information.

GUIDED PRACTICE for Examples 3 and 4 3. Without solving the linear system, tell whether it has one solution, no solution, or infinitely many solutions. x – 3y = –15 2x – 3y = –18 Equation 1 Equation 2 ANSWER one solution

GUIDED PRACTICE for Examples 3 and 4 4. WHAT IF? In Example 4, suppose a glossy print costs $3 more than a regular print. Find the cost of a glossy print. ANSWER A glossy print costs $8.