Question 636588

/ = a fraction
x/2 - y/3 = 5/6
x/5 - y/4 = 43/10
what is the solution to the system of equations by using substitution?


{{{x/2 - y/3 = 5/6}}} 


3x - 2y = 5 ------ Multiplying by LCD, 6 ----- eq (i)


{{{x/5 - y/4 = 43/10}}}


4x - 5y = 86 ----- Multiplying by LCD, 20 ------ eq (ii)


3x - 2y = 5 ------ eq (i)
4x - 5y = 86 ----- eq (ii)
- 15x + 10y = - 25 ----- Multiplying eq (i) by - 5 ------ eq (iii)
8x - 10y = 172 ----- Multiplying eq (ii) by 2 ------ eq (iv)
- 7x = 147 ----- Adding eqs (iv) & (iii)

x = {{{147/- 7}}}, or {{{highlight_green(- 21)}}}


- 63 - 2y = 5 ----- Substituting - 21 for x in eq (i)


- 2y = 5 + 63


- 2y = 68

y = {{{68/- 2}}}, or {{{highlight_green(- 34)}}}


You should be able to do your own check!!


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