SAT 2022 Test Prep | Solving System of Linear Equations | SAT Online Classes AMBiPi

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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

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

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

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

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

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

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

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.

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

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

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

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

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 

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.

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.

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?

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?

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?

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.

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.