Question 983857

a {{{linear}}} system of equations is when we have two or more {{{linear}}} equations

a{{{linear}}} equations are algebraic equations, such as {{{y = 4x + 3}}} for example, in which the variables are of the {{{first}}}{{{ degree}}} (that is, raised only to the first power) 

so, all other equations where the variables are of the higher degree are NOT {{{linear}}} equations, and such system is  NOT {{{linear}}} system  


you are given:

1.Which of the following are NOT linear systems. In each case explain why.

a.
{{{-2x+3y=7.5}}} 
{{{7x-2y=-2.5 }}}

as you can see,the variables are of the {{{first}}}{{{ degree}}} and this system is a linear system



b.
{{{x^2+y^2=4 }}}=>the variables are of the {{{second}}}{{{ degree}}}
{{{2x+2y=7}}}=>the variables are of the {{{first}}}{{{ degree}}}

and this system is a NOT linear system

 

c.
{{{5x-3y=12 }}}
{{{y=3x-8 }}}
as you can see,the variables are of the {{{first}}}{{{ degree}}} and this system is a linear system


d.
{{{4x-7y=-4 }}}
{{{3x+2xy=8}}}=>{{{y = (8-3x)/(2x)}}} which is a hyperbola

as you can see,the variables are of the {{{first}}}{{{ degree}}},but {{{3x+2xy=8}}} is not a linear equation, and  this system is NOT a linear system