The pair of linear equations $5x+4y=20$ and $10x+8y=16$, will have no solution. why?
Given: The pair of linear equations $5x+4y=20$ and $10x+8y=16$ will have no solution.
To do: To explain the reason why the given pair of linear equation has no solution.
Solution:
Here, $a_1=5,\ b_1=4,\ c_1=20$ and $a_2=10,\ b_2=8,\ c_2=16$.
$\frac{a_1}{a_2}=\frac{5}{10}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{4}{8}=\frac{1}{2}$
$\frac{c_1}{c_2}=\frac{20}{16}=\frac{5}{4}$
Therefore, we find that $\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$
Thus, There is no solution for the given pair of equation.
Related Articles
- Do the following pair of linear equations have no solution? Justify your answer.\( x=2 y \)\( y=2 x \)
- For which value(s) of $λ$, do the pair of linear equations $λx + y = λ^2$ and $x + λy = 1$ have no solution?
- For which value(s) of \( \lambda \), do the pair of linear equations \( \lambda x+y=\lambda^{2} \) and \( x+\lambda y=1 \) have no solution?
- Do the following pair of linear equations have no solution? Justify your answer.\( 2 x+4 y=3 \)\( 12 y+6 x=6 \)
- When the pair of linear equations $kx+4y=5$,$3x+2y=5$ is consistent only?
- Do the following pair of linear equations have no solution? Justify your answer.\( 3 x+y-3=0 \)\( 2 x+\frac{2}{3} y=2 \)
- For which value(s) of \( k \) will the pair of equations\( k x+3 y=k-3 \)\( 12 x+k y=k \)have no solution?
- (i) For which values of $a$ and $b$ does the following pair of linear equations have an infinite number of solutions?$2x + 3y =7$$(a – b)x + (a + b)y = 3a + b – 2$.(ii) For which value of $k$ will the following pair of linear equations have no solution?$(2k – 1)x + (k – 1)y = 2k + 1$.
- Find whether this pair of equations has a unique solution or an infinite number of solutions or no solution: $3x+5y=13$, $5x+3y=4$.
- On comparing the ratios $a_1,\ a_2,\ b_1,\ b_2$ and $c_1, c_2$, find out whether the following pair of linear equations are consistent, or inconsistent:$5x−3y=11; −10x+6y=−22$
- For which value(s) of $λ$, do the pair of linear equations $λx + y = λ^2$ and $x + λy = 1$ have a unique solution?
- Find the value(s) of \( p \) for the following pair of equations:\( -x+p y=1 \) and \( p x-y=1 \),if the pair of equations has no solution.
- On comparing the ratios $\frac{a_1}{a_2},\ \frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pair of linear equations is consistent or inconsistent: $5x-3y=11;\ -10x+6y=-22$
- For which value(s) of \( \lambda \), do the pair of linear equations \( \lambda x+y=\lambda^{2} \) and \( x+\lambda y=1 \) have a unique solution?
- For what value of $\alpha$, the system of equations $\alpha x+3y=\alpha -3$ $12x+\alpha y=\alpha$ will have no solution?
Kickstart Your Career
Get certified by completing the course
Get Started