In the following system of equation determine whether the system … - Vidyadip

Question

In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

$x - 2y = 8$

$5x - 10y = 10$

✓

Answer

Given
$x - 2y = 8$
$5x - 10y = 10$
To find: To determine whether the system has a uniqfue solution, no solution or infinitely many solutions
We know that the system of equations,
$a_1 x+b_1 y+c_1=0 $
$ a_2 x+b_2 y+c_2=0 $
For unique solution
$\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
For no solution
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
For infinitely many solution
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$
Here,
$\frac{1}{5}=\frac{-2}{-10}=\frac{8}{10}$
$\frac{1}{5}=\frac{1}{5}\neq\frac{4}{5}$
Since, $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ which means $\frac{1}{5}=\frac{1}{5}\neq\frac{4}{5}$ hence the system of equation has no solution.
Hence the system of equation has no solution.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Linear Equations in Two Variables→Linear Equations in Two Variables — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

A man on the deck of a ship is $10\ m$ above the water level. He observes that the angle of elevation of the top of a cliff is $45^\circ $ and the angle of depression of the base is $30^\circ $. Calculate the distance of the cliff from the ship and the height of the cliff.

In a right triangle $ABC$ in which $\angle\text{B}=90^{\circ},$ a circle is drawn with $AB$ as diameter intersecting the hypotenuse $AC$ at $P.$ Prove that the tangent to the circle at $P$ bisects
$BC.$

Solve the following quadratic equation:
$\frac{\text{3x}-4}{\text{7}}+\frac{\text{7}}{\text{3x}-4}=\frac{5}{2},$ $\text{x}\neq\frac{4}{3}$

Draw the graphs of the pair of linear equations $x - y + 2 = 0$ and $4x - y - 4 = 0$. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

If $2$ is added to each of two given numbers, their ratio becomes $1 : 2$. However, if $4$ is subtracted from each of the given numbers, the ratio becomes $5 : 11$. Find the numbers.

Solve for $x$ and $y$
$\frac{3}{\text{x}}-\frac{1}{\text{y}}+\text{9}=0,$
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=\text{5}$ $(\text{x}\neq0,\ \text{y}\neq0).$

Solve the following quadratic equation:
$\frac{1}{\text{2x}-3}+\frac{1}{\text{x}-5}=1\frac{1}{9},$ $\text{x}\neq\frac{3}{2},\ 5$

If $A(-1,3), B(1,-1)$ and $C(5,1)$ are the vertices of a triangle $A B C$, find the length of the median through $A$.

Find two consecutive positive even integers whose product is $288.$

Find the area of a trapezium whose parallel sides are $11\ cm$ and $25\ cm$ long and nonparallel sides are $15\ cm $and $13\ cm.$