Question 121696
The simple rule is: whatever you do to
one side of an equation, you have to do
to the other side
{{{6x + 3y = 30}}} and {{{2x + 3y = 18}}}
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What I see right away is I can divide both sides of the
1st equation by 3 without getting any fractions
{{{2x + y = 10}}}
Now, to get {{{y}}} alone on the left side, 
I subtract {{{2x}}} from both sides
{{{y = 10 - 2x}}}
Now I can substitute this {{{y}}} for the {{{y}}}
in the 2nd equation
{{{2x + 3(10 - 2x) = 18}}}
{{{2x + 30 - 6x = 18}}}
{{{30 - 4x = 18}}}
Now add {{{4x}}} to both sides
{{{30 = 4x + 18}}}
Now subtract {{{18}}} from both sides
{{{30 - 18 = 4x}}}
{{{12 = 4x}}}
divide both sides by {{{4}}}
{{{x = 3}}} answer
Now you can use either equation to find {{{y}}}
{{{2x + 3y = 18}}}
{{{2*3 + 3y = 18}}}
{{{6 + 3y = 18}}}
subtract {{{6}}} from both sides
{{{3y = 12}}}
{{{y = 4}}} answer
You can check these answers by substituting
back into original equations