$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

In the substitution method, the first step involves\: {
~ Adding equations
= Expressing one variable in terms of the other
~ Eliminating one variable
~ Verifying the solution
}

Which equation format is most convenient for the substitution method? {
~ Standard form (Ax + By \= C)
= Slope intercept form (y \= mx + b)
~ Quadratic form
~ Factored form
}

After substituting the value of one variable into another equation, you get\: {
~ A quadratic equation
= A single-variable linear equation
~ A system of equations
~ A graph
}

What is the main advantage of the substitution method? {
~ It works for non-linear equations
~ It always gives infinite solutions
= It systematically eliminates one variable
~ It avoids algebraic operations
}

What step is performed last in the substitution method? {
~ Verifying the solution
~ Expressing one variable in terms of another
= Substituting back to find the second variable
~ Adding the equations
}

//True or False

The substitution method can only be used when the equations are linear. {F}

Substitution is easier if one equation is already in the form y \= mx + b. {T}

The solution to a system of equations is where their graphs intersect. {T}

The equations are inconsistent if substitution leads to a false statement like 0 \= 5. {T}

Verification is not necessary if the values satisfy one of the equations. {F}

//Numericals



//Fill in the blanks

The substitution method reduces the system of equations to a single equation with _______. {
= One variable
~ Two variables
~ No variables
}

If the two equations represent the same line, the system has _______ solutions. {
~ No
~ Unique
= Infinite
}

When the system of equations is consistent, the substitution method always provides a _______ solution. {
~ False
= Valid
~ Graphical
}

Substituting the value of one variable into another equation is the _______ step. {
~ First
= Second
~ Final
}

A system of equations with no solution is _______. {
~ Consistent
= Inconsistent
~ Dependent
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Consistent System -> Equations with at least one solution
=Inconsistent System -> Equations with no solution
=Dependent System -> Equations with infinitely many solutions
=Verification -> Checking if values satisfy both equations
=Substitution Method -> Technique to solve systems algebraically
}



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