Question

How do you solve the system of equations `(7x)/2+(7y)/3=77/2` and `x/4+y/3=15/4`?

Answer 1

I have taken this to a point where you can take over.

Explanation:

The most straight forward way to deal with these ones is to lose the fractions.

Observe that the denominators 2, 3 and 4 are all factors of 12

`(7x)/2+(7y)/3=77/2" " ->" "(42x)/12+(28y)/12=462/12`

`" "=>42x+28y=462..Equation(1)`
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`x/4+y/3=15/4" "->" "(3x)/12+(4y)/12=45/12`

`" "=>3x+4y=45..Equation(2)`
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`color(blue)("Determine the value of "x)`

Observe that `4yxx7=28y` so we can relate the two equations to each other through `28y` and thus find `x`

Multiply equation(2) by 7 giving:

`" "21x+28y=315`

`" "=>28y=315-21x......Equation(2_a)`

Substitute for `28y` in equation(1) using equation(`2_a`)

`42x+(315-21x)=462`

`21x=147`

`color(blue)(x=147/21 = 7)`
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`color(red)("All you need to do now is solve for y by substitution")`
`color(red)("I will let you do that")`