Maths-

General

Easy

Question

What system of linear equations is represented by the lines shown?

$\begin{aligned} 3 x - 2 y = 6 \\ 3 x - 2 y = 12 \end{aligned}$
$\begin{aligned} 3 x - 2 y = 6 \\ 3 x + 2 y = 12 \end{aligned}$
$\begin{aligned} 2 x + 3 y = 6 \\ 2 x - 3 y = 12 \end{aligned}$
$\begin{aligned} - 2 x - 3 y = 6 \\ - 2 x + 3 y = 12 \end{aligned}$

The correct answer is: $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 x minus 2 y equals 6 end cell row cell 3 x minus 2 y equals 12 end cell end table$

HINT:-The given line passes through 2 sets of points so find the equation of lines from two-points form
Explanation : The two points is form for finding the equation of a line passing through the two points X1 ,Y1 and X2 ,Y2 as shown below
$y minus y 1 equals fraction numerator y squared minus y 1 over denominator x 2 minus x 1 end fraction left parenthesis x minus x 1 right parenthesis$
Step 1 : From observing the given graph .The 2 sets of points are {(2,0),(0,-3)} and {(4,0),(0,-6)}
Step 2 : Finding equation for line passing through {(2,0),(0,-3)}
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y minus y 1 equals fraction numerator y squared minus y 1 over denominator x 2 minus x 1 end fraction left parenthesis x minus x 1 right parenthesis end cell row cell y minus 0 equals fraction numerator negative 3 minus 0 over denominator 0 minus 2 end fraction left parenthesis x minus 2 right parenthesis end cell end table$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals fraction numerator negative 3 over denominator negative 2 end fraction left parenthesis x minus 2 right parenthesis end cell row cell 2 y equals 3 left parenthesis x minus 2 right parenthesis end cell end table$
$therefore 3 x minus 2 y equals 6$
Step 3 : Finding equation for line passing through {(4,0),(0,-6)}
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y minus y 1 equals fraction numerator y 2 minus y 1 over denominator x 2 minus x 1 end fraction left parenthesis x minus x 1 right parenthesis end cell row cell y minus 0 equals fraction numerator negative 6 minus 0 over denominator 0 minus 4 end fraction left parenthesis x minus 4 right parenthesis end cell row cell y equals fraction numerator negative 6 over denominator negative 4 end fraction left parenthesis x minus 4 right parenthesis end cell row cell y equals 3 over 2 left parenthesis x minus 4 right parenthesis end cell row cell 2 y equals 3 left parenthesis x minus 4 right parenthesis end cell row cell therefore 3 x minus 2 y equals 12 end cell end table$
∴ $3 x space minus space 2 y space equals space 6$ and $3 x space minus space 2 space y space equals space 12$ are the system of linear equations represented in the graph.

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What system of linear equations is represented by the lines shown?

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The correct answer is: $table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 x minus 2 y equals 6 end cell row cell 3 x minus 2 y equals 12 end cell end table$

Which of the following is equivalent to $2 open parentheses x squared minus x close parentheses plus 3 open parentheses x squared minus x close parentheses$ ?

Which of the following is equivalent to $2 open parentheses x squared minus x close parentheses plus 3 open parentheses x squared minus x close parentheses$ ?

$2 x minus y equals 8$
$x plus 2 y equals 4$
For the system of equations above, what is the value of x + y?

$2 x minus y equals 8$
$x plus 2 y equals 4$
For the system of equations above, what is the value of x + y?

Write the equivalent expressions for the following:
10(m + 10)

Write the equivalent expressions for the following:
10(m + 10)

A wave $straight y equals aSin invisible function application left parenthesis text ùt end text minus kx right parenthesis$ on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is

A wave $straight y equals aSin invisible function application left parenthesis text ùt end text minus kx right parenthesis$ on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is

If the velocity of planet is given by $straight v equals straight G to the power of 4 straight M to the power of straight b straight R to the power of straight prime$ then

If the velocity of planet is given by $straight v equals straight G to the power of 4 straight M to the power of straight b straight R to the power of straight prime$ then