884 CHAPTER 9 Systems and Matrices 9.1 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. The solution set of the following system is 511, ___26. -2x + 5y = 18 x + y = 5 2. The solution set of the following system is 51___, 026. 6x + y = -18 13x + y = -39 3. One way of solving the following system by elimination is to multiply equation (2) by the integer to eliminate the y-terms by direct addition. 14x + 11y = 80 (1) 2x + y = 19 (2) 4. To solve the system 3x + y = 4 (1) 7x + 8y = -2 (2) by substitution, it is easiest to begin by solving equation (1) for the variable and then substituting into equation (2), because no fractions will appear in the algebraic work. 5. If a system of two linear equations in two variables has graphs that coincide, there is/are _____________________ solution(s) to the system. (one / no / infinitely many) 6. If a system of two linear equations in two variables has graphs that are parallel lines, there is/are _____________________ solution(s) to the system. (one / no / infinitely many) Solve each system by substitution. See Example 1. 7. 4x + 3y = -13 -x + y = 5 8. 3x + 4y = 4 x - y = 13 9. x - 5y = 8 x = 6y 10. 6x - y = 5 y = 11x 11. 8x - 10y = -22 3x + y = 6 12. 4x - 5y = -11 2x + y = 5 13. 7x - y = -10 3y - x = 10 14. 4x + 5y = 7 9y = 31 + 2x 15. -2x = 6y + 18 -29 = 5y - 3x 16. 3x - 7y = 15 3x + 7y = 15 17. 3y = 5x + 6 x + y = 2 18. 4y = 2x - 4 x - y = 4 Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 19. 4x + y = -23 x - 2y = -17 20. 3x - y = -4 x + 3y = 12 21. 2x - 3y = -7 5x + 4y = 17 22. 4x + 3y = -1 2x + 5y = 3 23. 5x + 7y = 6 10x - 3y = 46 24. 12x - 5y = 9 3x - 8y = -18
RkJQdWJsaXNoZXIy NjM5ODQ=