Question

3. Greg is going to solve the system of linear equations below. First Equation: 74x10 Second Equation: 74x10 Which of the following would Greg NOT use to solve this system of equations?
A. Solve the second equation for y and then substitute the result into the first equation.
B. Multiply the first and second equation by -6 to eliminate the y variable.
C. Solve the first equation for y and then substitute the result into the second equation.
D. Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable.

4. When using elimination to solve 2x-3y = 4 7x+ 6y = -1 what would be a possible first step?
A. 4x – 6y = 8 7x + 6y = -l
B. x = 3/2y + 2 7x + 6y = -1
C. 2x -3y = 4 x = -6/7y – 1/7
D. y = 2/3x – 4/3 7x + 6y = -1

5 Sam purchased two bottles of water and three hot dogs at the ballpark for $8.50. Mary purchased one bottle of water and two hot dogs for $5.25. What system of equations could be solved to determine the prices in dollars of a hot dog (7x8 ) and a bottle of water (9x5 )?
A. 105x30
B105x30
C 93x30
D. 105x30

6. Given: 2x + y = 0 x – y = 6 What is the solution to the system of equations? A. (1, -2)
B. (2, -4)
C. (4, -2)
D.(5, -1)

7 Solve: 3x + y = -8 2x – y = 3
A (-1, -5)
B (3,3)
C (-2, -2)
D infinitely many solutions

Answer 1

4.) When solving a system of equations using elimination method, the first step is to make the coeffitient of one of the variables to be equal.
In option a, the coeffitient of variable y is made equal to 6 by multipling the first equation of the system by two.
Therefore, option A is the right answer.

6.) 2x + y = 0 . . . (1)
       x – y = 6 . . . (2)
(1) + (2) => 3x = 6 . . . (3)
x = 6/3 = 2.
From (2), 2 - y = 6
y = 2 - 6 = -4.
Therefore, solution is (2, -4)

7.) 3x + y = -8 . . . (1)
     2x – y = 3 . . . (2)
(1) + (2) => 5x = -5
x = -5 / 5 = -1
From (1), 3(-1) + y = -8
y = -8 + 3 = -5
Therefore, solution is (-1. -5)