Math Solving Systems Review Solution

Advanced Math Solving Systems Review Name: Solve each system using substitution or elimination. 1. y = 3x x + y = 4 x + 3x = 4 4x = 4 x = 1 y = 3(1) y = 3 2. 5x - y = 10 7x - 2y = 11 -2(5x - y = 10) -10x + 2y = -20 7x - 2y = 11 -3x = -9 x = 3 7(3) - 2y = 11 -2y = -10 y = 5 3. x + 4y = -8 2x - 4y = -16 x = -8 -8 + 4y = -8 4y = 0 y = 0 4. 2x + 5y = 3 -x + 3y = -7 2(2x + 5y = 3) 4x + 10y = 6 11y = -11 y = -1 2x + 5(-1) = 3 2x - 5 = 3 2x = 8 x = 4 5. 2x - 5y = -16 3y = 2x + 12 2x - 5y = -16 -2x + 3y = 12 -2y = -4 y = 2 2x - 5(2) = -16 2x - 10 = -16 2x = -6 x = -3 6. 4x + 3y = 180 x - y = 10 4x + 3y = 180 3(x - y = 10) 3x - 3y = 30 7x = 210 x = 30 30 - y = 10 y = 20 7. 4(2x - 3y = 1) 5(5x + 4y = 14) 8x - 12y = 4 15x + 12y = 42 23x = 46 x = 2 4 - 3y = 1 -3y = -3 y = 1 8. 2(2x + 3y = 9) 3(3x + 2y = 12) 4x + 6y = 18 -9x - 6y = -36 -5x = -18 x = 3.6 2(3.6) + 3y = 9 7.2 + 3y = 9 3y = 1.8 y = 0.6 Solve each system using substitution or elimination. 9. 5(0.7x + 0.5y = 2.9) 2(1.5x - 2.5y = -3.3) 3.5x + 2.5y = 14.5 3x - 5y = -6.6 13y = 65 y = 5 0.7x + 0.5(5) = 2.9 0.7x + 2.5 = 2.9 0.7x = 0.4 x = 2 10. -5(x - 4y = 11) x + 20y = -55 -5x + 20y = -55 x + 20y = -55 -4x = -110 x = 27.5 27.5 - 4y = 11 -4y = -16.5 y = 4.125 For #11-13, set up a system of 2 equations and solve. Use either substitution or elimination. 11. The sum of two numbers is 17 and their difference is 29. Find the numbers.   x + y = 17 x - y = 29 2x = 46 x = 23 23 + y = 17 y = -6 12. Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. Three hundred twenty-one tickets were sold altogether for $937.50. How many of each kind of ticket were sold?   3.50A + 2.50S = 937.50 A + S = 321 -2.5(A + S = 321) -2.5A - 2.5S = -802.50 3.50A + 2.50S = 937.50 A = 135 135 + S = 321 S = 186 13. Two complementary angles differ by 48°. What are the angles? x + y = 90° x - y = 48° 2x = 138° x = 69° 69 + y = 90° y = 21°