SOLUTION: find x and y systems : {{{ 3^(x+1) + 4(5^y) = 24 }}} and {{{ 3^x - 2(5^y) = -2 }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: find x and y systems : {{{ 3^(x+1) + 4(5^y) = 24 }}} and {{{ 3^x - 2(5^y) = -2 }}}      Log On


   

Question 793274: find x and y
systems : +3%5E%28x%2B1%29+%2B+4%285%5Ey%29+=+24+ and +3%5Ex+-+2%285%5Ey%29+=+-2+
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3%5E%28x%2B1%29+%2B+4%285%5Ey%29+=+24+ and +3%5Ex+-+2%285%5Ey%29+=+-2+
Divide both sides of the 1st expression by +3+
+3%5Ex+%2B+%284%2F3%29%2A%285%5Ey%29+=+8+
+3%5Ex+=+-%284%2F3%29%2A%285%5Ey%29+%2B+8+
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Substitute the right side into the 2nd equation
+-%284%2F3%29%2A%285%5Ey%29+%2B+8+-+2%285%5Ey%29+=+-2+
+-%284%2F3%29%2A%285%5Ey%29+-+2%285%5Ey%29+=+-10+
+-%282%2F3%29%2A%285%5Ey%29+-+5%5Ey+=+-5+
+5%5Ey+%2A%28+1+%2B+2%2F3+%29+=+5%0D%0A%7B%7B%7B+%285%2F3%29%2A5%5Ey+=+5+
(*) +5%5Ey+=+3+
+y%2Alog%285%29+=+log%283%29+
+y+=+log%283%29%2Flog%285%29+
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Now substitute (*) back into one of the equations
+3%5Ex+-+2%285%5Ey%29+=+-2+
+3%5Ex+-+2%2A3+=+-2+
+3%5Ex+=+4+
+x%2Alog%283%29+=+log%284%29+
+x+=+log%284%29%2Flog%283%29+
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I'll leave it to you to check answers