PRACTICE SOLVING SYSTEMS OF EQUATIONS FOR SAT

Problem 1 :

Which ordered pair (x, y) satisfies the system of equations below ?

5x+ y = 9

10x - 7y = -18

(a)  (-2, 19)    (b)  (1, 4)     (c) (3, -6)      (d)  (5, -1)

Solution

Problem 2 :

2x - 3y = -1

-x + y = -1

According to the systems of equations above, what is the value of x ?

Solution

Problem 3 :

-4x - 15y = -17

-x + 5y = -13

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution

Problem 4 :

0.3x - 0.7y = 1

kx - 2.8y  = 3

In the system of equations above, k is constant if the system has no solution, what is the value of k ?

Solution

Problem 5 :

-2x + 6y = 10

-3x + 9y = 18

How many solutions (x, y) are there to the system of the equations above. ?

(a)  Zero     (b)  one      (c) Two      (d)  More than two

Solution

Problem 6 :

3x - 2y = 6

9x - 6y = 2a

If the system of equations above has infinitely many solution, what is the value of a ?

Solution

Problem 7 :

x + ay = 5

2x + 6y = b

In the system equations above a and b are constants. If the system has one solution, which of the following could be the values of a and b ?

(a)  a = 3, b = 10    (b)  a = 3, b = -4

(c)  a = 3, b = 12     (d) a = 10, b = 3

Solution

Problem 1 :

x - 3y = 4

2(x - 1) - 6(y + 2) = -6

How many solutions (x, y) are there to the system of equations above ?

(a)  zero      (b)  One    (c)  Two     (d)  More than two

Solution

Problem 2 :

ax + 4y = 14

5x + 7y = 8

In the system of equations above, a is constant and x and y are variables, If the system has no solution, what is the value of a ?

(a)  20/7      (b)  35/4    (c)  -35/4    (d)  -20/7

Solution

Problem 3 :

ax + (1/2)y = 16

4x + 3y = 8

In the system of equations above, a is constant. If the system has no solution, what is the value of a ?

Solution

Problem 4 :

Paper West has produced 5000 kg of napkins. It continues to manufacture 350 kg of napkins per week. Northern Paper manufactures napkins at a rate of 1400 kg per month and has already produced 28000 kg. Assume one month has exactly four weeks.

a) Write a system of linear equations to represent the manufacturing of the napkins.

b) Explain how the number of solutions to the system relates to this situation.

Solution

Problem 5 :

For the linear system 2x + 3y = 12 and 4x + 6y = C, what value(s) of C will give the system

a) an infinite number of solutions?

b) no solution?

Solution

Problem 6 :

Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.

y = 3x + 14

y = –3x + 14

Solution

Problem 7 :

Without graphing the equations, decide whether the system has one solution, no solution, or infinitely many solutions.

5y = x – 9

4x – 10y = 18

Solution

Problem 1 :

3x + ky = 8

x + 4y = -1

If (x, y) is a solution to the system of equations above and k is constant, what is y in terms of k ?

(a)  5/(k - 12)     (b)  7/(k -4)     (c) 11/(k - 12)      (d)  9/(k -4)

Solution

Problem 2 :

x/(y +2) = 2

3(y - 5) - x = -16

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution

Problem 3 :

-2x - y = -9

5x - 2y = 18

Which of the following ordered pairs (x, y) fulfills the system of equations above ?

(a)  (-4, 1)    (b)  (2, 5)    (c)  (3, 3)     (d)  (4, 1)

Solution

Problem 4 :

-3x + 2y = 5

-9x + 6y = 18

The system of equations above has how many solutions (x, y) ?

(a)  Zero     (b)  One     (c)  Two      (d)  More than two

Solution

Problem 5 :

(1/3) x + (1/6) y = 5

(3/5) x + (1/5) y = -4

Which of the following ordered pairs (x, y) fulfills the system of equations above ?

(a)  (-50, 130)     (b)  (2, 26)    (c)  (5, 20)      (d)  (20, -10)

Solution

Problem 6 :

You and your friend are making 30 liters of sodium water. You have liters of 10% sodium and your friend has liters of 22% sodium. How many of your liters and how many of your friend's liters should you mix to make 30 liters of 15% sodium?

Solution