Podcast
Questions and Answers
What is the solution to the equations $ax + by = a - b$ and $bx - ay = a + b$?
What is the solution to the equations $ax + by = a - b$ and $bx - ay = a + b$?
- $x = -2, y = -2$
- $x = 1, y = -1$ (correct)
- $x = 1, y = 2$
- $x = 2, y = -1$
If $x = a$ and $y = b$ is the solution to the pair of equations $x - y = 2$ and $x + y = 4$, what are the values of $a$ and $b$?
If $x = a$ and $y = b$ is the solution to the pair of equations $x - y = 2$ and $x + y = 4$, what are the values of $a$ and $b$?
- 2, 1
- 1, 2
- 4, 6
- 3, 1 (correct)
If a pair of linear equations is consistent, how will the lines appear?
If a pair of linear equations is consistent, how will the lines appear?
- Always coincident
- Always intersecting
- Parallel
- Intersecting or coincident (correct)
How many solutions does the pair of equations $y = 0$ and $y = -7$ have?
How many solutions does the pair of equations $y = 0$ and $y = -7$ have?
For the equations $cx - y = 2$ and $6x - 2y = 3$ to have infinite solutions, what must be the value of $c$?
For the equations $cx - y = 2$ and $6x - 2y = 3$ to have infinite solutions, what must be the value of $c$?
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits are reversed. What is the number?
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits are reversed. What is the number?
For the equations $x - 2y = 3$ and $3x + ky = 1$ to have a unique solution, what condition must $k$ satisfy?
For the equations $x - 2y = 3$ and $3x + ky = 1$ to have a unique solution, what condition must $k$ satisfy?
If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, what is the value of $k$?
If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, what is the value of $k$?
A pair of linear equations has a unique solution where $x = 2$ and $y = -3$. Which system of equations satisfies this condition?
A pair of linear equations has a unique solution where $x = 2$ and $y = -3$. Which system of equations satisfies this condition?
The pair of equations $x = a$ and $y = b$ graphically represents lines that are:
The pair of equations $x = a$ and $y = b$ graphically represents lines that are:
For what value of $k$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?
For what value of $k$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?
One equation of a pair of dependent linear equations is $-5x + 7y = 2$. What could the second equation be?
One equation of a pair of dependent linear equations is $-5x + 7y = 2$. What could the second equation be?
Raju buys 7 books and 6 pens for $2750, and Anand buys 3 books and 5 pens of the same kind for $1300. What are the respective costs of a book and a pen?
Raju buys 7 books and 6 pens for $2750, and Anand buys 3 books and 5 pens of the same kind for $1300. What are the respective costs of a book and a pen?
A and B can together do a piece of work in 30 days. A worked for 16 days, and B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
A and B can together do a piece of work in 30 days. A worked for 16 days, and B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Flashcards
ax+by=a-b, bx-ay=a+b
ax+by=a-b, bx-ay=a+b
Solution: x=1, y=-1
x-y=2 and x+y=4 when x=a, y=b
x-y=2 and x+y=4 when x=a, y=b
a=3, b=1
Consistent Linear Equations
Consistent Linear Equations
Lines intersect or coincide
y = 0 and y = -7
y = 0 and y = -7
No Solution
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Infinite Solutions
Infinite Solutions
No Value
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Sum of Digits = 9, Reverse by +27
Sum of Digits = 9, Reverse by +27
36
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x – 2y = 3 and 3x + ky = 1 (unique solution)
x – 2y = 3 and 3x + ky = 1 (unique solution)
k ≠ -6
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3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel
3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel
k = -5/4
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x = 2 and y = -3 (unique solution)
x = 2 and y = -3 (unique solution)
x-4y-14 = 0, 5x - y - 13 = 0
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The pair of equations x = a and y = b
The pair of equations x = a and y = b
Intersecting at (a, b)
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3x – y + 8 = 0 and 6x – ky = –16 (coincident lines)
3x – y + 8 = 0 and 6x – ky = –16 (coincident lines)
k = 2
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-5x + 7y = 2 (dependent linear equations)
-5x + 7y = 2 (dependent linear equations)
10x – 14y = -4
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7 Books, 6 Pens = 2750; 3 Books, 5 Pens = 1300
7 Books, 6 Pens = 2750; 3 Books, 5 Pens = 1300
Book = 350, Pen = 50
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A+B in 30 days, A works 16 days, B finishes in 44
A+B in 30 days, A works 16 days, B finishes in 44
60 days
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- Multiple choice questions relate to pairs of linear equations in two variables
Question 1
- The solution to the equations ax+by=a-b and bx-ay=a+b is x=1, y=-1
Question 2
- Given x-y=2 and x+y=4, where x=a and y=b, the values are a=3 and b=1
Question 3
- If a pair of linear equations is consistent, the lines intersect or are coincident
Question 4
- The pair of equations y=0 and y=-7 has no solutions
Question 5
- For the equations cx – y = 2 and 6x – 2y = 3 to have infinite solutions, there is no value for c
Question 6
- A two-digit number has digits that sum to 9, and adding 27 reverses the digits; the number is 36
Question 7
- For the equations x – 2y = 3 and 3x + ky = 1 to have a unique solution, k cannot equal -6
Question 8
- If the lines 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then k = 15/4
Question 9
- A pair of linear equations with a unique solution for x = 2 and y = -3 is x – 4y – 14 = 0 and 5x – y – 13 = 0
Question 10
- With x = a and y = b, the pair of equations graphically represents lines intersecting at (a, b)
Question 11
- For the equations 3x – y + 8 = 0 and 6x – ky = –16 to represent coincident lines, k = 2
Question 12
- Given a pair of dependent linear equations where one equation is -5x + 7y = 2, a possible second equation is 10x – 14y = -4
Question 13
- If 7 books and 6 pens cost 2750 and 3 books and 5 pens of the same kind cost 1300, a book costs 350 and a pen costs 50
Question 14
- If A and B complete a piece of work together in 30 days, and A works for 16 days before B finishes the remaining work in 44 days, B alone would take 60 days to complete the whole work
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