Question 227306
1. Solve by the elimination method


{{{5r-7s=-3}}}  Equation A
{{{7r+5s=55}}}  Equation B.


Step 1.  Multiply by 5 in Equation A and Multiply by 7 in Equation B to eliminate the s-terms after adding the Equations now given below:


{{{25r-35s=-15}}}
{{{49r+35s=385}}}


Step 2.  Adding the above equations yield the following.


{{{74r=370}}}


Divide by 74 by both sides of the equation


{{{74r/74=370/74}}}


{{{r=5}}}


Step 3.  Substitute {{{r=5}}} into Equation A {{{5r-7s=-3}}}


{{{5*5-7s=-3}}}


{{{25-7s=-3}}}


Add 7s+3 to both sides of the equation


{{{25-7s+7s+3=-3+7s+3}}}


{{{28=7s}}}


Divide by 7 to both sides of the equation


{{{28/7=7s/7}}}


{{{4=s}}}


Step 4.  Substitute  {{{r=5}}} and {{{s=4}}} into  {{{7r+5s=55}}}


{{{7*5+5*4=55}}}


{{{55=55}}}


Step 5.  ANSWER:  {{{r=5}}} and {{{s=4}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J