Simple Simultaneous Equations in Two Variables

What does "simple simultaneous equations" mean?

In simple simultaneous equations, the two variables are of —

Two simple equations considered together are also called —

The equation $2x + y = 12$ is what type of equation?

How many solutions does the equation $2x + y = 12$ have?

In $2x + y = 12$, if $x = 3$, then $y =$ ?

In $x - y = 3$, if $x = 5$, then $y =$ ?

The common solution of the system $2x + y = 12,\; x - y = 3$ is —

The graph of a simple equation in two variables is —

A system of equations that has a solution is called —

A system of equations that has no solution is called —

If one equation cannot be expressed in terms of the other, the system is mutually —

If one equation is a constant multiple of the other, the system is mutually —

The number of solutions of a consistent and mutually independent system is —

The number of solutions of a consistent and mutually dependent system is —

The number of solutions of an inconsistent and mutually independent system is —

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually independent when —

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually dependent when —

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is inconsistent and mutually independent when —

If $c_1 = c_2 = 0$, the system $a_1 x + b_1 y = 0,\; a_2 x + b_2 y = 0$ is —

If $c_1 = c_2 = 0$ and $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$, the system has —

If $c_1 = c_2 = 0$ and $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$, the unique solution of the system is —

To check consistency from coefficient ratios alone (without comparing constant terms), the equations must satisfy —

For a consistent independent system in two variables, the graphs of the two equations —

The system $x + 3y = 1,\; 2x + 6y = 2$ is —

The number of solutions of $x + 3y = 1,\; 2x + 6y = 2$ is —

The system $2x - 5y = 3,\; x + 3y = 1$ is —

The system $3x - 5y = 7,\; 6x - 10y = 15$ is —

The number of solutions of $3x - 5y = 7,\; 6x - 10y = 15$ is —

The system $x - y = 4,\; x + y = 10$ is —

The number of solutions of $3x + 2y = 0,\; 6x + 4y = 0$ is —

The system $x - 2y + 1 = 0,\; 2x + y - 3 = 0$ is —

The unique solution of $3x + 2y = 0,\; 9x - 6y = 0$ is —

The system $5x - 2y = 6,\; 3x - y = 2$ is —

How many main methods of solving simple simultaneous equations are discussed in this chapter?

Which of the following is NOT a method of solving simple simultaneous equations?

Cross-multiplication method is also known as —

The English name of the graphical method is —

In which method is one variable expressed in terms of the other and then put into the second equation?

In which method are the equations multiplied so that absolute values of the coefficients of the same variable become equal, then added or subtracted?

Solving $2x + y = 8,\; 3x - 2y = 5$ by substitution, the value of $x$ is —

In the same system $2x + y = 8,\; 3x - 2y = 5$, the value of $y$ is —

The solution $(x, y)$ of $7x - 3y = 31,\; 9x - 5y = 41$ is —

The solution $(x, y)$ of $x + y = 7,\; x - y = 1$ is —

In the substitution method the first step is to —

The solution $(x, y)$ of $x + y = a + b,\; ax + by = a^2 + b^2$ is —

The solution of $x + y = 8,\; x - y = 4$ is —

The solution of $7x - 3y = 31,\; 9x - 5y = 41$ by elimination is —

The solution of $5x + 4y = 10,\; 4x + 5y = 8$ is —

The solution of $x + y = 5,\; x - y = 1$ is —

The solution of $2x + 3y = 12,\; x - y = 1$ is —

The solution of $3x + 2y = 13,\; x + y = 5$ is —

In the elimination method we —

To equalise the absolute values of the coefficients of one variable, we —

By cross-multiplication, for $a_1 x + b_1 y + c_1 = 0,\; a_2 x + b_2 y + c_2 = 0$, the value of $x$ is —

By cross-multiplication, the value of $y$ is —

In the cross-multiplication formula, the expression $a_1 b_2 - a_2 b_1$ appears as —

Before applying cross-multiplication the equations must be expressed in the form —

In $6x - y - 1 = 0,\; 3x + 2y - 13 = 0$, the values of $a_1, b_1, c_1$ respectively are —

In $6x - y - 1 = 0,\; 3x + 2y - 13 = 0$, the values of $a_2, b_2, c_2$ respectively are —

The solution of $6x - y = 1,\; 3x + 2y = 13$ by cross-multiplication is —

The solution of $3x - 4y = 0,\; 2x - 3y = -1$ by cross-multiplication is —

The solution $(x, y)$ of $\dfrac{x}{2} + \dfrac{y}{3} = 8,\; \dfrac{5x}{4} - 3y = -3$ is —

The solution $(x, y)$ of $ax - by = ab = bx - ay$ is —

The solution $(x, y)$ of $2x + 3y + 5 = 0,\; 4x + 7y + 6 = 0$ is —

The solution of $3x - 5y + 9 = 0,\; 5x - 3y - 1 = 0$ is —

For the system $ax - by = ab = bx - ay$ (Example 7), the value of $x + y$ is —

The solution of $x + 2y = 7,\; 2x - 3y = 0$ is —

For the system $ax - by = ab = bx - ay$ (Example 7), the value of $xy$ is —

Exercise 12.2 question 14, $y(3 + x) = x(6 + y),\; 3(3 + x) = 5(y - 1)$, is asked to be solved by which method?

The graph of a simple equation in two variables is —

To draw a straight line, at least how many points are needed?

If the graphs of the two equations coincide, the system is —

If the graphs of the two equations are parallel, the system is —

If two straight lines intersect at one point, the number of solutions of the system is —

The number of common points of two parallel lines is —

In Example 8, the graphs of $2x + y = 8,\; 3x - 2y = 5$ intersect at —

In Example 9, the graphs of $3x - y = 3,\; 5x + y = 21$ intersect at point $P$ whose coordinates are —

In Example 10, the graphical solution of $2x + 5y = -14,\; 4x - 5y = 17$ is —

In Example 11, the graphical solution of $3 - \dfrac{3x}{2} = 8 - 4x$ gives $x =$ —

The graphs of $2x + y = 3,\; 4x + 2y = 6$ are —

The graphs of $2x - y = 4,\; 4x - 2y = 12$ are —

In the equation $2x + y = 3$, if $x = 0$ then $y =$ —

In the equation $4x + 2y = 6$, if $y = 0$ then $x =$ —

If $2x - y = 8$ and $x - 2y = 4$, then $x + y =$ —

If $x + y = 6$ and $2x = 4$, then $y =$ —

The system $x - y - 4 = 0,\; 3x - 3y - 10 = 0$ is —

If the digit at the tens place is $x$ and units place is $y$, the two-digit number is —

After interchanging the digits of a two-digit number with tens digit $x$ and units digit $y$, the new number is —

In Example 12, the required number is —

The sum of digits of a two-digit number is $7$ and on interchanging the digits the new number exceeds the original by $9$. The number is —

The units digit of a two-digit number is $1$ more than thrice the tens digit, and the interchanged number equals $8$ times the sum of the digits. The original number is —

The difference of the digits of a two-digit number is $4$ and the sum of the number and its digit-reversal is $110$. The original number is (tens digit larger) —

The sum of two numbers is $31$ and their difference is $13$. The larger number is —

The sum of two numbers is $31$ and their difference is $13$. The smaller number is —

In Example 13, the present age of the father is —

In Example 13, the present age of the son is —

Let mother's present age be $x$ and the sum of her two daughters' ages be $y$. From the condition "mother's age is four times the sum of daughters' ages", the equation is —

"$8$ years ago, father's age was $8$ times son's age" gives — ($x$ = father's, $y$ = son's present age)

"After $10$ years, father's age will be twice son's age" gives —

If the numerator of a fraction is $x$ and denominator is $y$, the fraction is —

"If $1$ is added to numerator and denominator each, the fraction becomes $\dfrac{1}{2}$" gives the equation —

If $1$ is subtracted from numerator and $2$ is added to denominator, the new fraction is —