Is this a linear equation 5x+6y=3x-25x+6y=3x2?

2 Answers

Yes, it is a linear equation in two variables xx & yy.

Explanation:

The generalized linear equation in two variables xx & yy is given as

ax+by+c=0ax+by+c=0

The above equation shows a straight line on XYXY plane.

The given equation

5x+6y=3x-25x+6y=3x2

or 2x+6y+2=02x+6y+2=0

or x+3y+1=0x+3y+1=0

The above equation is in form of linear equation: ax+by+c=0ax+by+c=0

Jul 28, 2018

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Please read the explanation.

Explanation:

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Linear Equations are referred to as the equations of degree one,

where the variable's exponent ( or Power) is the value one.

Slope-Intercept Form:

This is the most common form of a linear equation.

It takes the form:

color(red)(y=mx+by=mx+b, where

color(red)(mm is the Slope or the Gradient

color(red)(bb is the y-intercept

General Form:

IF there are two variables in a linear equation it takes the form:

color(red)(Ax+By=CAx+By=C

To find the x-intercept, set color(blue)(y=0y=0

To find the y-intercept, set color(blue)(x=0x=0

color(blue)("Note :"Note :

For both of the above forms, we can construct a data table and create a graph.

Now, we will get back to the problem given to us:

color(red)(5x+6y = 3x-25x+6y=3x2

This is a linear equation with two variables

We can combine like terms and simplify the equation as
follows:

rArr 5x+6y=3x-25x+6y=3x2

Subtract color(red)(3x3x from both sides of the equation to balance the equation.

rArr 5x+6y-3x=3x-2-3x5x+6y3x=3x23x

rArr 5x+6y-3x=cancel(3x)-2-cancel(3x)

color(blue)(rArr 2x+6y=(-2)

Hence, we can conclude that the equation

color(red)(5x+6y = 3x-2

is indeed a linear equation.

y-intercept can be found by setting color(red)(x=0

rArr 2x+6y=(-2)

rArr 2(0)+6y=(-2)

rArr 6y= -2

Divide both sides by color(red)(6

rArr (6y)/6= (-2)/6

rArr y = -1/3

Hence we understand that color(blue)((0,-1/3) is the y-intercept

To find the x-intercept, set color(red)(y=0

rArr 2x+6y=(-2)

rArr 2x+6(0)=(-2)

rArr 2x=-2

Divide both sides of the equation by color(red)(2

rArr (2x)/2=(-2)/2

rArr (cancel 2x)/cancel 2=(-2)/2

rArr x = -1

Hence we understand that color(blue)((-1,0) is the x-intercept

We can verify these results using a graph as given below:

enter image source here

I hope this explanation is helpful.