SOLUTIONS FOR SYSTEMS OF EQUATIONS1. Which of the following statements would be the process that is used to describe solving a system of equation with 6 variables?Solving a 3 order systemSolving a 6 order systemSolving a systemSolving an order system2. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.2x - y = 72y = 4x - 14{}1 solutioninfinite3. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.x + y = 5x + y = 7{}1 solutioninfinite4. Which of the following points is a solution to the system of equations shown?y - x = -1x + y = -5(-3, -2)(-6, 1)(-2, -3)5. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.x + y = 4x - y = 0{}1 solutioninfinite6. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.3x + 2y = 6x - y = 2{}1 solutioninfinite7.Which of the following points is a solution to the system of equations shown?4x + y = 1y = x + 6(5, -1)(0, 6)(-1, 5)8.Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.x - y = 52x + y = 1{}1 solutioninfinite
Accepted Solution
A:
1. Solving an order system 2. Let us solve this one by combining the two equations:2x – y = 72y = 4x – 14 --> y = 2x – 7combine:2x – (2x – 12) = 72x – 2x + 7 = 70 + 7 = 77 = 7No variable at the end, therefore infinite solutions 3. From the given equations itself, we can see that this
is impossible to have solutions, therefore:{} 4. y – x = -1 --> y = x – 1x + (x – 1) = -52x – 1 = -5x = -2 y = x – 1 = -2 – 1 = -3(-2, -3) 5. x = yx + x = 42x = 4x = 2 = y(2, 2)1 solution 6. x – y = 2 --> x = 2 + y3 (2 + y) + 2y = 66 + 3y + 2y = 65y = 0y = 0 x = 2 + y = 2(0, 2)1 solution 7. 4x + (x + 6) = 15x + 6 = 15x = -5x = -1 y = x + 6 = -1 + 6 = 5(-1, 5) 8. x – y = 5 --> x = 5 + y2 (5 + y) + y = 110 + 2y + y = 13y = -9y = -3 x = 5 + y = 5 – 3 = 2(2, -3)
1 solution