Question 713659
Glad to be of help.
(1) {{{ y = 4x }}}
(2) {{{ y = 4x - 2 }}}
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Always look to see that the number of unknowns, 
( x and y in this case ), matches the number of 
equations. If so, then a solution is possible.
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The equations are in the slope-intercept form, which is
ideal for graphing.
In words, you have:
( y unknown ) = ( slope of the line )*( x unknown ) + ( y-intercept )
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y-intercept is where x = 0 
x-intercept is where y = 0
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(1) {{{ y = 4x }}}
(1) {{{ y = 4*0 }}}, so y-intercept is {{{y = 0}}}
and
(1) {{{ 0 = 4x }}}, so x-intercept is also {{{x = 0}}}
That means the line goes through the origin
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(2) {{{ y = 4x-2 }}}
(2) {{{ y = 4*0 - 2 }}}
(2) {{{ y = -2 }}}, so y-intercept is at {{{ y = -2 }}}
and
(2) {{{ 0 = 4x - 2 }}}
(2) {{{ 4x = 2 }}}
(2) {{{ x = 1/2 }}}, so x-intercept is at {{{ x = 1/2 }}}
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Here's the plots of the lines which shows the above data:
{{{ graph( 400, 400, -5, 5, -5, 5, 4x, 4x-2 ) }}}
Note that the slopes are the same, so they don't
intersect, and there can be no solution.
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There is no solution when:
(a) The lines are parallel ( this case ), or
(b) The equations are actually the same, as the following:
{{{ y = 3x + 11 }}}
{{{ 2y = 6x + 22 }}}
If the divide the 2nd line by {{{2}}}, you get the 1st line
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Hope all this helps. Good luck