$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 linear equations by the elimination method? {
~ Solve for x
~ Solve for y
= Make the coefficients of one variable equal
~ Verify the solution
}

Which operation is commonly used to eliminate a variable? {
~ Addition
~ Subtraction
~ Multiplication
= All of the above
}

If x \= 2 and y \= 1 solve the equations, which step should follow next? {
~ Check using a graph
= Verify by substituting into the original equations
~ Add both equations again
~ Multiply both equations again
}

How can coefficients of variables be adjusted for elimination? {
~ Multiply one equation
~ Multiply both equations
~ Divide both equations
= Either A or B
}

What happens if the two equations are inconsistent? {
= No solution
~ Infinite solutions
~ Unique solution
~ Graph is a parabola
}

//True or False

The elimination method involves eliminating one variable at a time. {T}

To eliminate a variable, the coefficients of that variable must always be equal. {T}

The solution to x+y\=3 and x-y\=1 is x\=1; y\=2. {F}

Adding equations with opposite-signed variables eliminates the variable. {T}

Verifying the solution by substituting values is not necessary. {F}

//Numericals



//Fill in the blanks

To solve equations by elimination, we _______ the coefficients of one variable. {
~ Add
= Equalize
~ Subtract
~ Ignore
}

If x \= 2 and y \= 1;  the solution satisfies the _______ equations. {
= Original
~ Modified
~ Multiplied
~ Divided
}

The elimination method is helpful because it removes _______ from the equations. {
~ Constants
= One variable
~ Coefficients
~ Both variables
}

The next step after finding values of variables is _______. {
~ Graphing
= Verifying
~ Dividing
~ Subtracting
}

If the lines represented by equations are coincident, the system has _______ solutions. {
~ No
= Infinite
~ Unique
~ Undefined
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Adjust coefficients -> Multiply one or both equations
=Eliminate variable -> Add or subtract equations
=Solve the remaining equation -> Find the value of one variable
=Verify solution -> Check values in the original equations
}



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