$CATEGORY: Maths - TicTacLearn/3. Pair of linear equations in two variables/3. Pair of linear equations in two variables--Algebric Methods of Solving a Pair of Linear Equations

//Multiple Choice

What is the first step in solving a pair of linear equations by the elimination method? {
= Multiply one or both equations to make coefficients of a variable the same
~ Add both equations directly
~ Substitute values of x and y randomly
~ None of the above
}

Which of the following is a necessary condition for using the elimination method? {
~ Both equations must have integer coefficients
= At least one variable must have the same coefficient in both equations
~ One equation must be in slope-intercept form
~ Both equations must be in quadratic form
}

Solve using elimination\: 1) 2x+3y\=12 & 2) 4x-3y\=6. What is the value of x? {
= 3
~ 2
~ 4
~ 5
}

After eliminating one variable, what should you do next? {
~ Write the equation in slope-intercept form
= Solve for the remaining variable
~ Substitute back into the original equation
~ None of the above
}

Solve using elimination\: 1) 5x-2y\=10 & 2) 3x+2y\=6. What is the value of x? {
~ 1
= 2
~ 3
~ 4
}

What happens if both variables get eliminated and we get a false statement like 0 \= 5? {
~ The system has infinitely many solutions
= The system has no solution
~ The system has a unique solution
~ The system is not linear
}

If elimination gives an identity like 0 \= 0, what does it mean? {
= The system has infinitely many solutions
~ The system has no solution
~ The system has a unique solution
~ The system is inconsistent
}

The elimination method works best when\: {
~ One equation is quadratic
= Coefficients of one variable are already the same
~ Variables are already eliminated
~ One equation has fractions
}

Solve using elimination\: 1) 6x+4y\=20 & 2) 3x+2y\=10 {
~ No solution
= Infinite solutions
~ Unique solution (x \= 2, y \= 2)
~ Unique solution (x \= 4, y \= 0)
}

The elimination method is also called\: {
~ Substitution method
= Addition method
~ Graphical method
~ None of the above
}

//True or False

The elimination method is always possible for linear equations. {T}

Elimination is the best method when coefficients of variables are already equal. {T}

The elimination method always gives a unique solution. {F}

Parallel lines represent dependent equations. {F}

If we eliminate a variable and get a false statement, the system is inconsistent. {T}

If the coefficients of one variable are already the same, elimination is not needed. {F}

The elimination method is also called the "multiplication method." {F}

The elimination method can be used for quadratic equations. {F}

If elimination leads to a true identity, there are infinite solutions. {T}

The elimination method works by substituting values. {F}

//Numericals

Solve using the elimination method\: 1) 2x+3y\=12 & 2) 4x-3y\=6. What is the value of x? {
= 3
~ 2
~ 4
~ 5
}

Solve using the elimination method\: 1) 3x+2y\=7 & 2) 5x-2y\=3. What is the value of x? {
= 2
~ 3
~ 4
~ 5
}

Solve using the elimination method\: 1) 5x-y\=9 & 2) 3x+y\=5. What is the value of y? {
~ -2
= 2
~ 3
~ 4
}

Solve using the elimination method\: 1) 6x-5y\=4 & 2) 4x+5y\=20. What is the value of x? {
~ 3
~ 4
= 2
~ 1
}

Solve using the elimination method\: 1) 2x+5y\=20 & 2) 3x-5y\=5. What is the value of y? {
~ 2
~ 3
~ 4
= 5
}

Solve using the elimination method\: 1) 7x+4y\=19 & 2) 5x-4y\=5. What is the value of x? {
~ 3
= 2
~ 4
~ 1
}

Solve using the elimination method\: 1) 4x+3y\=18 & 2) 6x-3y\=6. What is the value of x? {
= 3
~ 4
~ 5
~ 6
}

Solve using the elimination method\: 1) 3x-2y\=8 & 2) 5x+4y\=2. What is the value of y? {
= -2
~ -3
~ -4
~ -1
}

Solve using the elimination method\: 1) 5x+3y\=27 & 2) 2x-3y\=6. What is the value of x? {
~ 5
= 4
~ 3
~ 2
}

Solve using the elimination method\: 1) 8x-7y\=1 & 2) 6x+7y\=23. What is the value of x? {
~ 2
~ 3
= 4
~ 5
}

//Fill in the blanks

In the elimination method, we eliminate ________ variable at a time. {
= One
~ Two
~ Three
~ None
}

To eliminate a variable, we make the coefficients of that variable ________. {
~ Different
= Equal
~ Zero
~ Infinity
}

The elimination method is useful for solving ________ equations. {
= Linear
~ Quadratic
~ Cubic
~ Exponential
}

If two equations are dependent, they have ________ solutions. {
~ One
~ No
= Infinite
~ Two
}

If two equations are inconsistent, they have ________ solution(s). {
~ One
= No
~ Infinite
~ None of the above
}

The elimination method is also known as the ________ method. {
~ Substitution
= Addition
~ Graphical
~ None
}

The equation 3x+4y\=10  and 6x+8y\=20  are ________ equations. {
~ Parallel
= Dependent
~ Inconsistent
~ None
}

The elimination method involves ________ the equations. {
~ Adding
~ Subtracting
= Both a and b
~ None
}

If two equations have the same coefficients but different constants, they are ________. {
~ Consistent
= Inconsistent
~ Dependent
~ None
}

The solution of two coincident lines is ________. {
~ No solution
~ Unique solution
= Infinite solutions
~ None
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
= 3x+4y\=10, 6x+8y\=20 -> Unique Solution
= 2x+3y\=12, 4x-3y\=6 -> Unique Solution
= x+y\=5, x+y\=10 -> Unique solution
= 5x-2y\=10, 3x+2y\=6 -> Unique solution
}



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