Presentation on theme: "Solve the linear system."— Presentation transcript:
1 Solve the linear system. 1. 4x – 3y = 152x – 3y = 9ANSWER(3, –1)2. –2x + y = –82x – 2y = 8ANSWER(4, 0)
2 3. You can row a canoe 10 miles upstream in 2 3. You can row a canoe 10 miles upstream in 2.5 hours and 10 miles downstream in 2 hours. What is the average speed of the canoe in still water?ANSWER4.5 mi/h
3 Multiply one equation, then add EXAMPLE 1Multiply one equation, then addSolve the linear system:6x + 5y = 19Equation 12x + 3y = 5Equation 2SOLUTIONSTEP 1Multiply Equation 2 by –3 so that the coefficients of x are opposites.6x + 5y = 196x + 5y = 192x + 3y = 5–6x – 9y = –15STEP 2Add the equations.–4y = 4
4 Multiply one equation, then add EXAMPLE 1Multiply one equation, then addSTEP 3Solve for y.y = –1STEP 4Substitute –1 for y in either of the original equations and solve for x.2x + 3y = 5Write Equation 2.2x + 3(–1) = 5Substitute –1 for y.2x + (–3) = 5Multiply.2x = 8Subtract –3 from each side.x = 4Divide each side by 2.
5 Multiply one equation, then add EXAMPLE 1Multiply one equation, then addANSWERThe solution is (4, –1).CHECKSubstitute 4 for x and –1 for y in each of the original equations.Equation 1Equation 26x + 5y = 192x + 3y = 56(4) + 5(–1) = 19?2(4) + 3(–1) = 5?19 = 195 = 5
6 Multiply both equations, then subtract EXAMPLE 2Multiply both equations, then subtractSolve the linear system:4x + 5y = 35Equation 12y = 3x – 9Equation 2SOLUTIONSTEP 1Arrange the equations so that like terms are in columns.4x + 5y = 35Write Equation 1.–3x + 2y = –9Rewrite Equation 2.
7 EXAMPLE 2Multiply both equations, then subtractSTEP 2Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10.4x + 5y = 358x + 10y = 70–3x + 2y = –9–15x +10y = –45STEP 3Subtract: the equations.23x = 115STEP 4Solve: for x.x = 5
8 Multiply both equations, then subtract EXAMPLE 2Multiply both equations, then subtractSTEP 5Substitute 5 for x in either of the original equations and solve for y.4x + 5y = 35Write Equation 1.4(5) + 5y = 35Substitute 5 for x.y = 3Solve for y.ANSWERThe solution is (5, 3).
9 Multiply both equations, then subtract EXAMPLE 2Multiply both equations, then subtractCHECKSubstitute 5 for x and 3 for y in each of the original equations.Equation 1Equation 24x + 5y = 352y = 3x – 94(5) + 5(3) = 35?2(3) = 3(5) – 9?35 = 356 = 6ANSWERThe solution is (5, 3).
10 GUIDED PRACTICEfor Examples 1 and 2Solve the linear system using elimination.6x – 2y = 11.–2x + 3y = –5ANSWERThe solution is (–0.5, –2).
11 GUIDED PRACTICEfor Examples 1 and 2Solve the linear system using elimination.2x + 5y = 32.3x + 10y = –3ANSWERThe solution is (9, –3).
12 GUIDED PRACTICEfor Examples 1 and 2Solve the linear system using elimination.3x – 7y = 53.9y = 5x + 5ANSWERThe solution is (–10, –5).
13 EXAMPLE 3Standardized Test PracticeDarlene is making a quilt that has alternating stripes of regular quilting fabric and sateen fabric. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. Which system of equations can be used to find the amount x (in yards) of regular quilting fabric and the amount y (in yards) of sateen fabric she purchased?x + y = 16Ax + y = 16Bx + y = 764x + 6y = 76x + y = 16Dx + y = 76C4x + 6y = 166x + 4y = 76
14 EXAMPLE 3Standardized Test PracticeSOLUTIONWrite a system of equations where x is the number of yards of regular quilting fabric purchased and y is the number of yards of sateen fabric purchased.Equation 1: Amount of fabricx+y=16
15 Standardized Test Practice EXAMPLE 3Standardized Test PracticeEquation 2: Cost of fabric4766+=yxThe system of equations is:x + y = 16Equation 14x + 6y = 76Equation 2ANSWERADCBThe correct answer is B.
16 GUIDED PRACTICEfor Example 3SOCCER A sports equipment store is having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccer ball bags for $155. Another soccer coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag.4.ANSWERsoccer ball $14.50, soccer ball bag: $5
17 Daily Homework QuizSolve the linear system using elimination.x + 3y = 12–2x + y = 4ANSWER(0, 4)2. –3x + 2y = 75x – 4y = –15ANSWER(1, 5)3. –7x – 3y = 114x – 2y = 16ANSWER(1, –6)
18 Daily Homework QuizA recreation center charges nonmembers $3 to use the pool and $5 to use the basketball courts. A person pays $42 to use the recreation facilities 12 times. How many times did the person use the pool.4.ANSWER9 times