Question 158543
solving the equation by algebraic means, we get
{{{(3*x-2*y)=4}}}
{{{(-6*x+4*y)=7}}}
solving for y in the first equation, we get
{{{y=((3*x)/2)-2)}}}
substituting this for y in the second equation, we get
{{{y=(-6*x+4)+4*(3*x/2 - 2) = 7}}}
this becomes
{{{y=-6*x + 6*x - 8 = 7}}}
since the x cancels out we are left with
-8=7
which means there is no solution.
looking at both equations in y = slope intercept form, we see
{{{y=(3*x/2)-2}}}
and
{{{y=(6*x/4)+(7/4)}}}
general form of the slope intercept form of the equation is y=m*x+b
where m is the slope and b is the y intercept when x = 0.
slope of the first equation is 3/2
slope of the second equation is 6/4 which simplifies to 3/2.
slopes are equal so lines are parallel.
solving by equation below shows that right away.
{{{graph(600,600,-5,5,-15,15,(3x-4)/2,(6x+7)/4)}}}