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Test: Simultaneous Equations - SAT MCQ


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10 Questions MCQ Test Mathematics for SAT - Test: Simultaneous Equations

Test: Simultaneous Equations for SAT 2024 is part of Mathematics for SAT preparation. The Test: Simultaneous Equations questions and answers have been prepared according to the SAT exam syllabus.The Test: Simultaneous Equations MCQs are made for SAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Simultaneous Equations below.
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Test: Simultaneous Equations - Question 1

Solve the following simultaneous equations:
x + y = 5
2x + y = 8

Detailed Solution for Test: Simultaneous Equations - Question 1

Multiply the first equation by 2 and subtract it from the second equation to eliminate y:
(2x + y) - (2x + 2y) = 9 - 10
-y = -1
y = 1
Substitute y in the first equation:
x + 2 = 5
x = 5 - 2
x = 3

Test: Simultaneous Equations - Question 2

Solve the following system of equations:
2x + y = 8
x - 3y = -5

Detailed Solution for Test: Simultaneous Equations - Question 2

We can solve this system using either the substitution or elimination method. Let's use the elimination method by multiplying the first equation by 3 and adding it to the second equation:

6x + 3y = 24
x - 3y = -5
7x = 19

So, x = 19/7. Substituting this value into the first equation, we get:

2(19/7) + y = 8

Solving for y, we get:

y = 18/7

Therefore, the answer is A) x = 19/7, y = 18/7.

Test: Simultaneous Equations - Question 3

Solve the following system of equations:
3x - y = 7
2x + 3y = 1

Detailed Solution for Test: Simultaneous Equations - Question 3

We can use the substitution method by solving one equation for one variable and substituting it into the other equation. Solving the first equation for y, we get:

y = 3x - 7

Substituting this into the second equation, we get:

2x + 3(3x - 7) = 1

Simplifying and solving for x, we get:

x = 2

Substituting this value into the first equation, we get:

3(2) - y = 7

Solving for y, we get:

y = -1

Therefore, the answer is A) x = 2, y = -1.

Test: Simultaneous Equations - Question 4

Solve the following system of equations:
5x + 3y = 11
-2x + y = -5

Detailed Solution for Test: Simultaneous Equations - Question 4

Test: Simultaneous Equations - Question 5

What is the solution of the system of equations:
2x + 3y = 10
4x + 6y = 20

Detailed Solution for Test: Simultaneous Equations - Question 5

We can solve this system of equations by using the elimination method. Multiply the first equation by 2,
we get 4x + 6y = 20.
This is the same as the second equation.
Therefore, the system has infinitely many solutions, and the correct answer is (d) No solution.

Test: Simultaneous Equations - Question 6

Find the value of x and y for the system of equations:
3x + 4y = 10
2x + 5y = 8

Detailed Solution for Test: Simultaneous Equations - Question 6



Test: Simultaneous Equations - Question 7

Solve the system of equations:
5x + 6y = 32
2x - 3y = 5

Detailed Solution for Test: Simultaneous Equations - Question 7

We can solve this system of equations by using the elimination method. Multiply the second equation by 3,
we get 6x - 9y = 15.
Adding this equation to the first equation,
we get 11x = 47. Solving for x,
we get x = 47/11.
Substituting x into the second equation,
we get y = -3/11.
The correct answer is (none of the above), x = 47/11, y = -3/11.

Test: Simultaneous Equations - Question 8

Which method can be used to solve the following simultaneous equations?

(i) 2x - y = 5
(ii) 3x + y = 11

Detailed Solution for Test: Simultaneous Equations - Question 8

The given simultaneous equations have oppositely signed y terms.
By adding both equations, we can eliminate the y variable and solve for x.

Test: Simultaneous Equations - Question 9

What is the value of x in the following simultaneous equations?

(i) 4x + 2y = 8
(ii) 2x - y = 5

Detailed Solution for Test: Simultaneous Equations - Question 9

Multiply the second equation by 2 to match the coefficients of x in both equations: 4x - 2y = 10.
Now add both equations: 8x = 18, and x = 9/4.

Test: Simultaneous Equations - Question 10

Which method can be used to solve the following simultaneous equations?

(i) x - y = 3
(ii) 3x + 2y = 1

Detailed Solution for Test: Simultaneous Equations - Question 10

The first equation can be easily rearranged to x = y + 3.
Substituting this into the second equation will eliminate the x variable and allow us to solve for y.

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