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Maths-

General

Easy

Question

-3x + y = 6
ax + 2y = 4
In the system of equations above, a is a constant. For which of the following values of a does the system have no solution?

-6
-3
3
6

hint Hint:

Hint:

If two linear equation in two variable has no solution then,

$a subscript 1 over a subscript 2 equals b subscript 1 over b subscript 2 not equal to c subscript 1 over c subscript 2$ .

The correct answer is: -6

Explanation:

We have given a linear equation in two variables $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative 3 x plus y equals 6 end cell row cell a x plus 2 y equals 4 end cell end table text . end text$ .

We have to find the value of a, $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 x plus b subscript 1 x equals c subscript 1 end cell row cell a subscript 2 x plus b subscript 2 y equals c subscript 2 end cell end table$ , for which the given system has no solution.

If we have two linear equation, , then for no solution, condition is

$a subscript 1 over a subscript 2 equals b subscript 1 over b subscript 2 not equal to c subscript 1 over c subscript 2$
Step 1 of 1:
We have system of linear of equation $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative 3 x plus y equals 6 end cell row cell a x plus 2 y equals 4 end cell end table$ .
Here,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals negative 3 semicolon b subscript 1 equals 1 semicolon c subscript 1 equals 6 end cell row cell a subscript 2 equals a semicolon b subscript 2 equals 2 semicolon c subscript 2 equals 4 end cell end table$
Now apply the condition,
$a subscript 1 over a subscript 2 equals b subscript 1 over b subscript 2 not equal to c subscript 1 over c subscript 2$
So,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator negative 3 over denominator a end fraction equals 1 half end cell row cell a equals negative 6 end cell end table$
Hence, Option A is correct.

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