Question 855480
{{{system (3x + y = 9, 5x + 4y = 22)}}} solved in tiny steps.

STEP 1:
Start by multiplying both sides of the equal sign by a convenient number for one equation,
and doing the same for the other equation, if needed.
How do you choose the convenient number(s)?
You choose them so as to "eliminate" one variable in the next step.
There is more than one way to choose, and one way may look easier than another.
{{{3x + y = 9}}}--->{{{(4)(3x + y)=(4)*9}}}--->{{{12x +12y=+36}}}
{{{5x + 4y = 22}}}--->{{{(-1)(5x + 4y)=(-1)*22}}}--->{{{-5x - 4y = -22}}}
 
STEP 2:
Add together left sides and right sides
{{{matrix(3,4,"+12 x","+12 y","=",+36,-5 x,-4 y,"=",-22,7x,"+0 y","=",14)}}}
That "eliminated" {{{y}}} because we ended up with
{{{7x=14}}} .
 
STEP 3:
Solve for the variable not eliminated.
{{{7x=14}}}--->{{{x=14/7}}}--->{{{highlight(x=2)}}}
 
STEP 4:
Substitute the value found for the variable in one of the equations.
Which one?
Again, there are choices, and one way may look easier than another.
{{{3x + y = 9}}} looks better to me, because there is no coefficient in front of the {{{y}}} .
{{{system(3x + y = 9,x=2)}}} --->{{{3*2+y=9}}}--->{{{6+y=9}}}

STEP 5:
Solve for the originally "eliminated" variable.
{{{6+y=9}}}--->{{{y=9-6}}}--->{{{highlight(y=3)}}}