$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 is used to solve\: {
~ Linear equations in one variable
= Linear equations in two variables
~ Quadratic equations
~ Cubic equations
}

What is the first step in the substitution method? {
~ Substituting one equation into the other
= Solving for one variable in terms of another
~ Adding the equations
~ Graphing the equations
}

If one equation is y \= 2x + 3 and second equation is x + y \= 10 substituting y gives\: {
~ 2x + 3 \=10
= x + (2x + 3) \= 10
~ y \= 2x + 3 + 10
~ x + y \= 0
}

The substitution method avoids\: {
~ Graphical representation
~ Algebraic manipulation
~ Finding intersections
~ Solving equations
}

Which scenario indicates no solution in a pair of linear equations? {
~ Coincident lines
= Parallel lines
~ Intersecting lines
~ All of the above
}

//True or False

In the substitution method, one variable is expressed in terms of the other. {T}

Linear equations solved using substitution always have a unique solution. {F}

If two equations represent the same line, they have no solution. {F}

The substitution method works only for equations in slope-intercept form. {F}

The substitution method is less effective than the graphical method. {F}

//Numericals



//Fill in the blanks

The substitution method solves _______ equations in two variables. {
~ quadratic
= linear
~ exponential
}

If the equations are y \= 3x + 2 and x + y \= 7; substituting y gives ____. {
= x + (3x + 2) \= 7
~ 3x + 2 \= 7
~ y \= 7 - x
}

For parallel lines, the ratio of coefficients of variables is _______. {
= Equal
~ Unequal
~ Proportional
}

If a system of equations has infinitely many solutions, the lines are _______. {
~ Parallel
~ Intersecting
= Coincident
}

The substitution method converts two equations into _______. {
= A single-variable equation
~ A quadratic equation
~ A linear system
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Substitution method -> Method of solving by replacing one variable
=Parallel lines -> Lines that never intersect
=Coincident lines -> Lines with infinitely many solutions
=Unique solution -> One solution exists.
}



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