Math Connections Systems of Equations Reteach - Cobb Learning
Math Connections Systems of Equations Reteach - Cobb Learning
Math Connections Systems of Equations Reteach - Cobb Learning
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Name Date ClassLESSON11-6<strong>Reteach</strong><strong>Systems</strong> <strong>of</strong> <strong>Equations</strong>Two or more equations considered together form a system <strong>of</strong> equations.To solve a system <strong>of</strong> equations, you can use a method <strong>of</strong> substitution.Solve the system: y 3xy 5x 20Use the first equation to y 5x 20 second equationsubstitute for y in the second equation. 3x 5x 20 Replace y with 3x.Solve the resulting equation for x. 2x 20 Combine like terms. 2x20 2 2Divide by 2.x 10Substitute the x-value into the firsty 3xequation to get the corresponding y-value. y 3(10) 30Check: Substitute both values in each <strong>of</strong> the original equations.y 3x y 5x 2030 3(10) 30 5(10) 20 x 10 and y 3030 30 30 50 20 So, the solution <strong>of</strong> the20 20 system is (10, 30).Solve and check this system.1. y 2x6x y 16Use the first equation to substitute fory in the second equation.6x 2x16Solve the resulting equation for x.8x 16 8 x 1 68 8x 2Substitute the x-value to get thecorresponding y-value.4Check both values in each <strong>of</strong> theoriginal equations.y 2x 6x y 162 2( ) 6( ) 164 4 212 4So, the ordered pairthe solution <strong>of</strong> the system.24 1616 16 isy 2xy 2(2) 4Copyright © by Holt, Rinehart and Winston.49 Holt <strong>Math</strong>ematicsAll rights reserved.
Name Date ClassLESSON11-6<strong>Reteach</strong><strong>Systems</strong> <strong>of</strong> <strong>Equations</strong> (continued)Sometimes, you first have to solve one equation for a variable.Solve the system: y 3x 7x 2y 4Solve the first equation for y. y 3x 73x 3x Subtract 3x.y 7 3xSubstitute for y in the x 2y 4 second equationsecond equation. x 2(7 3x) 4 Replace y with 7 3x.Solve for x. x 14 6x 4 Distributive property5x 14 4 Combine like terms.14 14 Subtract 14. 5x510 5Divide by 5.x 2Substitute the x-value into y 3x 7the first equation to get the y 3(2) 7corresponding y-value. y 6 7y 6 6 7 6y 1Check: Substitute both values in each <strong>of</strong> the original equations.y 3x 7 x 2y 4 x 2 and y 11 3(2) 7 2 2(1) 4 The solution <strong>of</strong> the7 7 4 4 system is (2, 1).Solve and check this system.4. y 2x 0x 2y 6Solve the first equation for y.y 2x 0y Use the result to substitute for y inthe second equation.x 2y 6x 2( ) 62x2xSolve the resulting equation for x.Substitute the x-value to get thecorresponding y-value. 2xy 4Check:y 2x 0 x 2y 6x 2So, the ordered pair (3, 4)is the solution <strong>of</strong> the system.Copyright © by Holt, Rinehart and Winston.50 Holt <strong>Math</strong>ematicsAll rights reserved.
LESSON11-6Practice B<strong>Systems</strong> <strong>of</strong> <strong>Equations</strong>Solve each system <strong>of</strong> equations.1. y 2x 4y x 1(3,2)3. y 2x 1y 3x 6( 1, 3)5. y 2x 3y 2x 1no solution7. x y 05x 2y 3( 1,1)9. 2x 3y 64x 6y 12infinite number11. The sum <strong>of</strong> two numbers is 24. The second number is 6 lessthan the first. Write a system <strong>of</strong> equations and solve itfind the number.x y 24; y x 6; (15, 9)15. Kerry and Luke biked a total <strong>of</strong> 18 miles in one weekend.Kerry biked 4 miles more than Luke. Write a system <strong>of</strong> equationsand solve it to find how far each boy biked.x y 18; x 4 y; (7, 11); Luke biked 7 miles, andKerry biked 11 miles2. y x 10y x 2(4,6)4. y 2xy 12 x(4,8)6. y 3x 1y x 1(1,2)8. 2x 3y 02x y 8(3,2)10. 6x y 142x 3y 6(3, 4)LESSON11-6Practice C<strong>Systems</strong> <strong>of</strong> <strong>Equations</strong>Solve each system <strong>of</strong> equations.1. y 3x 1 2. 2x 3y 12y 2x x 4y 53. x 2y 8 4. 2x y 74x y 5 3x 4y 8(2, 3)5. y 0.4x 6. 2x y 4y 0.8x 2 1 2 y x 27. 2y 5x 5 8. y 1 4 x 17y 3x 32 1 5 , 2 5 (5, 2)(1, 5)x 4y 49. 2x 3y 3 10. 4x y 33y 5 2x 4x y 1no solution11. The sum <strong>of</strong> two numbers is 381. Their differenceis 155. Find the two numbers.12. The theater group sold adult and student tickets for the play.They sold a total <strong>of</strong> 560 tickets. Each adult ticket was $8 andeach student ticket was $3.50. The group took in a total <strong>of</strong>$3166. How many <strong>of</strong> each type <strong>of</strong> ticket were sold for the play?292 student tickets; 268 adult tickets13. The cost <strong>of</strong> 20 blank recordable CDs and 6 music CDs is $80.70.The cost <strong>of</strong> 30 blank recordable CDs and 4 music CDs is $66.30.Find the cost <strong>of</strong> each blank recordable CD and each music CD.blank recordable CD: $0.75; music CD: $10.95(3, 2)(4, 1)There are an infinite number <strong>of</strong> solutions.(0, 1) 1 2 , 1 (113, 268)Copyright © by Holt, Rinehart and Winston.47 Holt <strong>Math</strong>ematicsAll rights reserved.Copyright © by Holt, Rinehart and Winston.48 Holt <strong>Math</strong>ematicsAll rights reserved.LESSON11-6<strong>Reteach</strong><strong>Systems</strong> <strong>of</strong> <strong>Equations</strong>Two or more equations considered together form a system <strong>of</strong> equations.To solve a system <strong>of</strong> equations, you can use a method <strong>of</strong> substitution.Solve the system: y 3xy 5x 20Use the first equation to y 5x 20 second equationsubstitute for y in the second equation. 3x 5x 20 Replace y with 3x.Solve the resulting equation for x. 2x 20 Combine like terms. 2x20 2 2Divide by 2.x 10Substitute the x-value into the firstequation to get the corresponding y-value.y 3xy 3(10) 30Check: Substitute both values in each <strong>of</strong> the original equations.y 3x y 5x 2030 3(10) 30 5(10) 20 x 10 and y 3030 30 30 50 20 So, the solution <strong>of</strong> the20 20 system is (10, 30).Solve and check this system.1. y 2x6x y 16Use the first equation to substitute fory in the second equation.6x 2x 16Solve the resulting equation for x.8x 16 8 x 1 68 8x 2Substitute the x-value to get thecorresponding y-value.y 2xy 2( 2 ) 4Check both values in each <strong>of</strong> theoriginal equations.y 2x 6x y 164 2( 2 ) 6( 2 ) 4 164 4 12 4So, the ordered pair (2, 4)the solution <strong>of</strong> the system. 1616 16 Copyright © by Holt, Rinehart and Winston.49 Holt <strong>Math</strong>ematicsAll rights reserved.isLESSON11-6<strong>Reteach</strong><strong>Systems</strong> <strong>of</strong> <strong>Equations</strong> (continued)Sometimes, you first have to solve one equation for a variable.Solve the system: y 3x 7x 2y 4Solve the first equation for y. y 3x 73x 3x Subtract 3x.y 7 3xSubstitute for y in the x 2y 4 second equationsecond equation. x 2(7 3x) 4 Replace y with 7 3x.Solve for x. x 14 6x 4 Distributive property5x 14 4 Combine like terms.14 14 Subtract 14.Substitute the x-value into y 3x 7the first equation to get the y 3(2) 7corresponding y-value. y 6 7y 6 6 7 6y 1 5 x5 10 Divide by 5.5x 2Check: Substitute both values in each <strong>of</strong> the original equations.y 3x 7 x 2y 4 x 2 and y 11 3(2) 7 2 2(1) 4 The solution <strong>of</strong> the7 7 4 4 system is (2, 1).Solve and check this system.4. y 2x 0x 2y 6Solve the first equation for y.y 2x 0y 2xUse the result to substitute for y inthe second equation.x 2y 6x 2( 2x ) 6Solve the resulting equation for x.x 2Substitute the x-value to get thecorresponding y-value.y 2xy 2(2)y 4Check:y 2x 0 x 2y 6So, the ordered pair (2, 4)is the solution <strong>of</strong> the system.Copyright © by Holt, Rinehart and Winston.50 Holt <strong>Math</strong>ematicsAll rights reserved.Copyright © by Holt, Rinehart and Winston.66 Holt <strong>Math</strong>ematicsAll rights reserved.
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