Find four different solutions of equation x + 2y = 6.

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4. Linear Equations in Two Variables

easy

Find four different solutions of the equation $x + 2y = 6.$

Option A

Option B

Option C

Option D

Solution

By inspection, $x=2,\, y=2$ is a solution because for $x=2,\, y=2$

$x+2 y=2+4=6$

Now, let us choose $x = 0$. With this value of x, the given equation reduces to $2y = 6$ which has the unique solution $y = 3$. So $x = 0$, $y = 3$ is also a solution of $x + 2y = 6$. Similarly, taking $y = 0$, the given equation reduces to $x = 6$. So, $x = 6$, $y = 0$ is a solution of $x + 2y = 6$ as well. Finally, let us take $y = 1$. The given equation now reduces to $x + 2 = 6$, whose solution is given by $x = 4$. Therefore, $(4,\, 1)$ is also a solution of the given equation. So four of the infinitely many solutions of the given equation are :

$(2,\,2)$, $(0,\,3)$, $(6,\,0) $ and $ (4,\,1)$

Standard 9

Mathematics

Draw the graph and linear equations in two variables : $x + y = 4$

medium

Give the geometric representations of $2x + 9 = 0$ as an equation

$(i)$ in one variable

$(ii)$ in two variables

hard

Write each of the following as an equation in two variables :

$(i)$ $x=-\,5$

$(ii)$ $y=2$

$(iii)$ $2x=3$

$(iv)$ $5y=2$

easy

For each of the graphs given in Fig. select the equation whose graph it is from the choices given below :

$(a)$ For Fig. $(i)$,

$(i)$ $x+y=0$ $(ii)$ $y=2 x$   $(iii)$ $y=x$   $(iv)$ $y=2 x+1$

$(b)$ For Fig. $(ii)$,

$(i)$ $x+y=0$ $(ii)$ $y=2 x$   $(iii)$ $y=2x+4$   $(iv)$ $y=x-4$

$(c)$ For Fig. $(iii)$,

$(i)$ $x+y=0$ $(ii)$ $y=2 x$   $(iii)$ $y=2x+1$   $(iv)$ $y=2 x-4$

easy

Give the equations of two lines passing through $(2, \,14)$. How many more such lines are there, and why ?

medium

Find four different solutions of the equation $x + 2y = 6.$

Solution

Similar Questions

Draw the graph and linear equations in two variables : $x + y = 4$

Give the geometric representations of $2x + 9 = 0$ as an equation $(i)$ in one variable $(ii)$ in two variables

Write each of the following as an equation in two variables : $(i)$ $x=-\,5$ $(ii)$ $y=2$ $(iii)$ $2x=3$ $(iv)$ $5y=2$

Give the equations of two lines passing through $(2, \,14)$. How many more such lines are there, and why ?

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Give the geometric representations of $2x + 9 = 0$ as an equation

$(i)$ in one variable

$(ii)$ in two variables

Write each of the following as an equation in two variables :

$(i)$ $x=-\,5$

$(ii)$ $y=2$

$(iii)$ $2x=3$

$(iv)$ $5y=2$