Welcome to **AMBiPi (Amans Maths Blogs)**. In this article, you will get * SAT 2022 Test Prep | System of Linear Equations | SAT Online Classes AMBiPi*.

### SAT 2022 Math Multiple Choice Practice Questions

#### System of Linear Equations Multiple Choice Questions with Answer Keys

**SAT Test Prep Question No 1:**

z + w – 3 = k and

6z – 10w = 8

Consider the system of equations above, where k is a constant. For which value of k are there infinitely many (w, z) solutions?

**Option A** : -19/5

**Option B** : 5

**Option C** : 8

**Option D** : None of these

**Show/Hide Answer Key**

**Option D : none of these**

**SAT Test Prep Question No 2:**

-5x – 4y = 2a and

4x – 5y = 2

Which of the following choices of a will result in a system of linear equations with exactly one solution?

**Option A** : a can be any number

**Option B** : a can be any number except 0.8

**Option C** : a can be any number except -0.8

**Option D** : a = 0.8

**Show/Hide Answer Key**

**Option A : a can be any number**

**SAT Test Prep Question No 3:**

In 1.70p – 0.34q = 0 and

0.17(q + 1) – 0.85(p – 1) = 0

Consider the system of equations above. How many (p, q) solutions does this system have?

**Option A** : 0

**Option B** : 1

**Option C** : Infinite

**Option D** : none of these

**Show/Hide Answer Key**

**Option A : 0**

**SAT Test Prep Question No 4:**

3s + 2t – 3 = c and

-7s – 5t = 4

Consider the system of equations above, where c is a constant. For which value of c is there exactly one (s, t) solution where s=−1?

**Option A** : -4.8

**Option B** : 4 4/7

**Option C** : 18

**Option D** : None of these

**Show/Hide Answer Key**

**Option A : -4.8**

**SAT Test Prep Question No 5:**

0.7a − 0.8b = −0.1 and

a− 1.4 = −6(b−0.1)

Consider the system of equations above. If (a, b) is the solution to the system, then what is the value of the sum of a and b?

**Option A** : -0.5

**Option B** : -0.1

**Option C** : 0.1

**Option D** : 0.5

**Show/Hide Answer Key**

**Option D : 0.5**

**SAT Test Prep Question No 6:**

6(1 − a) = 3(a − b) + 1 and

4(b − 2) = 3a

Consider the system of equations above. If (a, b) is the solution to the system, then what is the value of a − b?

**Option A** : -1276/243

**Option B** : 29/9

**Option C** : 44/27

**Option D** : 1276/243

**Show/Hide Answer Key**

**Option D : 1276/243**

**SAT Test Prep Question No 7:**

−4a − 5b − 4 = −21

−2b + 5a − 11 = −9

Consider the system of equations above. What is the value of −2a−b?

**Option A** : -5

**Option B** : -1/3

**Option C** : 1/3

**Option D** : 5

**Show/Hide Answer Key**

**Option A : -5**

**SAT Test Prep Question No 8:**

2x − 1 = y

3x − 1 = y

Consider the system of equations above. Which of the following statements about this system is true?

**Option A** : There is only one (x, y) solution and y is positive

**Option B** : There is only one (x, y) solution and y is negative

**Option C** : There are infinitely many (x, y) solutions.

**Option D** : There are no (x, y) solutions.

**Show/Hide Answer Key**

**Option B : There is only one (x, y) solution and y is negative.**

**SAT Test Prep Question No 9:**

44(j + 2k) = 12

22k = −11j + 16

Consider the system of equations above. How many solutions (j,k) does this system have?

**Option A** : 0

**Option B** : Exactly 1

**Option C** : Exactly 2

**Option D** : Infinite many

**Show/Hide Answer Key**

**Option A : 0**

**SAT Test Prep Question No 10:**

5x − 2y = 6

10x − 4y = c

Which of the following choices of c will result in a system of linear equations with no solutions?

**Option A** : c = 12

**Option B** : c can be any number other than -12

**Option C** : c can be any number other than 12

**Option D** : c can be any number

**Show/Hide Answer Key**

**Option C: c can be any number other than 12**

**SAT Test Prep Question No 11:**

−x = −6y − 7

x − 6y = k

Consider the system of equations above. Which of the following choices of k will result in a system of equations with infinitely many solutions?

**Option A** : Any number

**Option B** : Any number except 12

**Option C** : 7

**Option D** : -7

**Show/Hide Answer Key**

**Option C : 7**

**SAT Test Prep Question No 12:**

6p/5 + kq = 4/5 and

q = 3p/5 – 2/5

Consider the system of equations above, where k is a constant. For which value of k is there no (p, q) solutions?

**Option A** : -2

**Option B** : 0

**Option C** : 2

**Option D** : none of these

**Show/Hide Answer Key**

**Option D : none of these**

**SAT Test Prep Question No 13:**

Consider the system of equations above, where a is a constant. For which value of a is (x, y) = (4, 1) a solution?

**Option A** : -34/27

**Option B** : -1/27

**Option C** : 34/9

**Option D** : none of these

**Show/Hide Answer Key**

**Option D : none of these**

**SAT Test Prep Question No 14:**

Consider the system of equations above. Which of the following statements about this system is true?

**Option A** : There is only one (x, y) solution and x+y is positive

**Option B** : There is only one (x, y) solution and x+y is negative

**Option C** : There are infinitely many (x, y) solutions

**Option D** : There are no (x, y) solutions.

**Show/Hide Answer Key**

**Option C : There are infinitely many (x, y) solutions.**

**SAT Test Prep Question No 15:**

Consider the system of equations above. Which of the following statements is true?

**Option A** : There is only one (x, y) solution and x+y is positive

**Option B** : There is only one (x, y) solution and x+y is negative

**Option C** : There are infinitely many solutions

**Option D** : There are no solutions.

**Show/Hide Answer Key**

**Option B : There is only one (x, y) soution and x+y is negative.**

### SAT 2022 Math Grid-in Practice Questions

#### System of Linear Equations Grid-in Choice Questions with Answer Keys

**SAT Test Prep Question No 16:**

−11y = 6(z + 1) − 13y

4y − 24 = c(z − 1)

For what value of c does the above system of linear equations in the variables y and z have infinitely many solutions?

**Show/Hide Answer Key**

**Correct Answer : 12**

**SAT Test Prep Question No 17:**

a(y – 1/3) + x/2 = 0 and 3x − y − 1 = 0

Consider the system of equations above, where a is a constant. For which value of a are there infinitely many (x, y) solutions?

**Show/Hide Answer Key**

**Correct Answer : -3/2**

**SAT Test Prep Question No 18:**

ay = 2x + 1 and y = 2x + 2

Consider the system of equations above, where a is a constant. Find the value of for which (x, y) has no solutions?

**Show/Hide Answer Key**

**Correct Answer : 1**

**SAT Test Prep Question No 19:**

5.2s + 0.1r = 0 and 0.7(r + 0.2) + 3.2 = -3s

Consider the system of equations above, if (r, s) is the solution to system, then what is the value of (r + s)? Round the answer to the nearest tenth.

**Show/Hide Answer Key**

**Correct Answer : -5.1**

**SAT Test Prep Question No 20:**

-6.4x = 4y + 2.1 and ky = 3.2x = 5.8 For what value of k does the above system, then what is the value of (r + s)? Round the answer to the nearest tenth.

**Show/Hide Answer Key**

**Correct Answer : -5.1**