Example 1 Solve the linear system. Solving a Linear System by Graphing y+x = 5 y = 2x2x 1 – SOLUTION STEP 1 Graph both equations as shown. STEP 2 Estimate the point of intersection using the graph. It appears that the point of intersection is. () 2, 3 Equation 1 Equation 2

Example 1 Solving a Linear System by Graphing STEP 3 Check whether is a solution by substituting 2 for x and 3 for y in each of the equations. () 2, 3 Equation 2 Equation 1 y+x = 5 y = 2x2x 1 – – = ? = ? () 22 5 = 53 = 3 The solution is ( ).). 2, 3 ANSWER

Example 2 Multiple Choice Practice You can buy a skating park membership for a fee of $100. Each park visit costs members $8 and nonmembers $12. After how many visits will the total costs for a member and a nonmember be equal? SOLUTION STEP 1 Use verbal models to write equations representing each option.

Example 2 Multiple Choice Practice Equation 1 (members) y = 8x8x Equation 2 (nonmembers) y = 12x

Example 2 Multiple Choice Practice STEP 2 Graph the equations and in only the first quadrant because negative values of x and y do not make sense in this situation. y = 8x8x y = 12x STEP 3 ( ).). 25, 300 Estimate the point of intersection. The graphs appear to intersect at

Example 2 Multiple Choice Practice ANSWER The correct answer is D. After 25 visits, the total costs are equal. STEP 4 Check the solution = ( 258 ) + Equation 1 checks. 300 = ( 2512 ) Equation 2 checks.

Guided Practice for Examples 1 and 2 Solve the linear system by graphing. Then check the solution. 1. y = 3 x – + y = 7 x– ANSWER 2 – ( 5,5, )

Guided Practice for Examples 1 and 2 Solve the linear system by graphing. Then check the solution. 2. yx = 2 – 2y2y6x6x = 8 – ANSWER 1 – ( 1,1, )

Guided Practice for Examples 1 and 2 Solve the linear system by graphing. Then check the solution. 3. y = 5 x– 3x3x + 3 y= –– ANSWER 6 – 1,1, )( –

Guided Practice for Examples 1 and 2 4. WHAT IF? In Example 2, suppose the membership fee is $60. After how many visits will the total costs for a member and nonmember be equal? ANSWER 15 visits