$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

Solve using substitution\: x + y \= 8; x - y \= 2 {
=x \= 5 ; y \= 3
~x \= 6; y \= 2
~x \= 4; y \= 4
~x \= 3; y \= 5
}

If x \= 3y -2 and 2x + y \= 12; find y. {
=y \= 4
~y \= 3
~y \= 2
~y \= 1
}

What does it mean if substitution results in 5 \= 5? {
~A unique solution exists
~No solution exists
=Infinite solutions exist
~None of the above
}

Solve x\= 2y + 1 and 3x-y \= 7 {
~x \= 3; y \= 1
=x \= 4; y \= 2
~x \= 5; y \= 3
~x \= 1; y \= -1
}

Substitution leads to 0 \= -3. What does it mean? {
=No solution
~Unique solution
~Infinite solutions
~Cannot be determined
}

//True or False

Substitution can only be used when one equation is already solved for a variable. {F}

If substitution leads to a constant equation (like 3 \= 3); the system has infinite solutions. {T}

The substitution method works for both linear and quadratic equations. {T}

Substitution is not possible if both equations are in standard form (like ax + by \= c) {F}

The substitution method is always faster than the elimination method. {F}

//Fill in the blanks

Substitution requires expressing one variable in terms of _______. {
~constants
=another variable
~coefficients
}

A pair of equations with infinite solutions represents _______ lines. {
~parallel
=coincident
~perpendicular
}

The result 0 \= 0 in substitution indicates _______. {
~unique solution
~no solution
=infinitely many solutions
}

Substitution is most efficient when one equation is already solved for _______. {
~coefficients
~constants
=a variable
}

If substitution results in an inconsistent equation, the lines are _______. {
=parallel
~perpendicular
~overlapping
}


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