Question 203405
<pre>
Solve by the elimination method.
7r+3s=38
3r+7s=66
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21r+ 9s = 114
21r+49s = 462
</pre>
Except for the "-" in front of the 49 and the missing "s" after the 49, you are good so far. Now we can subtract the second equation from the first one. As a result, the 21r terms will cancel which is the key to the Elimination Method. After subtracting we have:
{{{-40s = -348}}}
Now we solve this equation. Divide by -40:
{{{s = 348/40 = 87/10}}}
Now we substitute this value in for "s" into one of the original equations:
{{{7r + 3(87/10) = 38}}}
{{{7r + 261/10 = 38}}}
Multiply by 10 to eliminate the fraction:
{{{70r + 261 = 380}}}
Subtract 261 from both sides:
{{{70r = 119}}}
Divide by 70:
{{{r = 119/70 = 17/10}}}
So the solution is
r = 17/10 and s = 89/10