The system of equations x+2y=3 and 3x+6y=a-2 | vedclass

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(D) Given the system of equations $x+2y=3$ and $3x+6y=a-2$. For a system of linear equations $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$ to have no solution,t

Vedclass · Accepted Answer

$a 
eq 11$

Vedclass · Answer

(D) Given the system of equations $x+2y=3$ and $3x+6y=a-2$. For a system of linear equations $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$ to have no solution,the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$. Comparing the given equations with the standard form,we have $a_1=1, b_1=2, c_1=3$ and $a_2=3, b_2=6, c_2=a-2$. Substituting these values into the condition: $\frac{1}{3} = \frac{2}{6} 
eq \frac{3}{a-2}$. Since $\frac{1}{3} = \frac{2}{6}$ is always true,we focus on the inequality $\frac{1}{3} 
eq \frac{3}{a-2}$. Cross-multiplying gives $a-2 
eq 3 	imes 3$,which simplifies to $a-2 
eq 9$. Therefore,$a 
eq 11$.

The system of equations $x+2y=3$ and $3x+6y=a-2$ has no solution if:

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