Question 577732
So you have the system of linear equations
{{{system(4x+3y=9,3x+4y=12)}}}
and you are trying to solve it by "elimination."
{{{4x+3y=9}}} is equivalent to {{{(-3)(4x+3y)=(-3)*9}}} --> {{{-12x-9y=-27}}}
If the expression {{{4x+3y}}} is equal to {{{9}}},
the value of (-3) times that expression will be (-3) times {{{9}}}.
Multiplying both sides of the equation by the same non-zero number, gives you another equivalent equation, with exactly the same solutions.
{{{3x+4y=12}}} is equivalent to {{{4(3x+4y)=4*12}}} --> {{{12x+16y=48}}}
If you did those transformations and got the equivalent equations
{{{-12x-9y=-27}}} and {{{12x+16y=48)}}},
you are on the right path.
Next you would add those equations and keep the resulting equation
{{{-12x-9y+12x+16y=-27+48)}}} --> {{{7y=21}}} --> {{{highlight(y=3)}}}
along with one of your original equations:
{{{system(y=3,4x+3y=9)}}}
At that point, you would substitute the value of {{{y}}} into the second equation and find that {{{highlight(x=0)}}}