Question 29875
{{{ y=4x-6 }}} and {{{ 3y=7-3x }}}  Substitute 4x-6 from the firt equation into the second.
{{{ 3y=7-3x }}}
{{{ 3(4x-6)=7-3x }}}  distribute the 3
{{{ 12x-18 = 7-3x }}} add 3x to both sides
{{{ 15x -18 = 7 }}} add 18 to both sides
{{{ 15x = 25 }}} divid both sides by 15
{{{ x = 25/15 }}} reduce
{{{ x = 5/3}}}
plug x = 5/3 back into the first equation
{{{ y=4x-6 }}}
{{{ y=4(5/3)-6 }}}
{{{ y = (20/3) - 6 }}} change 6 to 18/3 (common denom)
{{{ y = (20/3) - 18/3 }}} subtract
{{{ y = 2/3 }}}
solution : (5/3, 2/3) 

now by elimination:
{{{ y=4x-6 }}} and {{{ 3y=7-3x }}} we will deal with the first equation
solve for the form Ax+By=C
{{{ y=4x-6 }}} subtract 4x from both sides
{{{ -4x+y=-6 }}} multiply by -1 to make the x value positive
{{{ 4x-y=6 }}} now solve the second equation so that it is in the same form
{{{ 3y=7-3x }}} add 3x to both sides
{{{ 3x+3y=7 }}} now lets look at both equations stacked on ontop of the other.
4x - 1y = 6
3x + 3y = 7
if we multiply all parts of the first equation by three we get ...
12x - 3y = 18
3x + 3y = 7
looking at the y values .. they will cancel when we add the two equations and get ...
15x + 0y = 25 the y is gone now ...
15x = 25  divide both sides by 15
x = 25/15 or 5/3
substitute this back into ANY of the equations to find y