<PRE><B>Question 410101</B>
solve this system of equations by the addition method:
6x + 9y = -41
15x - 6y = 40
:
Multiply the 1st equation by 2, multiply the 2nd equation by 3, results
12x + 18y = -82
45x - 18y = 120
--------------------addition eliminates y, find x
57x = 38
x = {{{38/57}}} 
:
Find y using the 1st original equation
6({{{38/57}}}) + 9y = -41
{{{228/57}}} + 9y = -41
9y = -41 - {{{228/57}}}
9y = -{{{2337/57}}} - {{{228/57}}}
9y = -{{{2565/57}}}
which is, fortunately:
9y = -45
y = {{{(-45)/9}}}
y = -5
:
Summarize: x={{{38/57}}}; y = -5
:
:
See if that works in the 2nd equation
15x - 6y = 40
15({{{38/57}}}) - 6(-5) = 40
{{{570/57}}}) + 30 = 40
10 + 30 = 40; so these solutions for x and y are correct</PRE>