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Maths-

SAT

Easy

Question

$y equals 1 half x plus 5$
One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?

y = 2x + 5
$y = \frac{1}{2} x + 5$
$y = \frac{1}{2} x - 4$
y = -2x + 5

The correct answer is: $y equals 1 half x minus 4$

Two equations have no solution if linear equations
$a subscript 1 x plus b subscript 1 y equals c subscript 1 & space a subscript 2 x plus b subscript 2 y equals c subscript 2$ satisfy
$a subscript 1 over a subscript 2 equals b subscript 1 over b subscript 2 not equal to c subscript 1 over c subscript 2$
Here line equation is $fraction numerator negative 1 over denominator 2 end fraction x plus y equals 5$
$a subscript 1 equals fraction numerator negative 1 over denominator 2 end fraction$ b1 = 1 c1 = 5
Let other equation be $a subscript 2 x plus b subscript 2 y equals c subscript 2$
$rightwards double arrow a subscript 2 equals fraction numerator negative 1 over denominator 2 end fraction$ b2=1 c2 $not equal to$ 5
we see it in option c

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