Question

Is (3,8) a solution to this system of equations?
y=53x+3y=73x+1

yes or no

Answer 1

`\textcolor{green}{ \textbf{no}}`

`x = (1)/(10) , y = (83)/(10)`

Explanation:

y=53x+3

y=73x+1

Solve y = 53x + 3 for equ 2 | equ means equation

`\sf \: 53x + 3 = 73x + 1`

Substract 73x from both sides

`\sf \: 53x - 73x + 3 = 1`

Solve 53x - 73x

`\sf - 20x + 3 = 1`

Substract 3 from both sides

`\sf - 20x + 3 - 3 = 1 - 3`

Solve

`\sf \: - 20x = - 2`

Divide both sides by -20

`\sf (- 20x)/( - 20)= ( - 2)/( - 20)`

Solve

`\sf x = (1)/(10)`

`\sf -------------------------------------------------`

Substitute x = 1/10 into equ 1

`\sf y = 53x + 3`

Insert x = 1/10

`\sf y = 53( (1)/(10) ) + 3`

multiply 54 by the numerator which is 1

`\sf \: y = (53)/(10) + 3`

Turn 3 to 3/1

`\sf \: y = (53)/(10) + (3)/(1)`

L.C.M = 10

`\sf y = ( (53)/(10) * 10 \: + \: (3)/(1) * 10 )/(10)`

Simplify

`\sf \: y = (53 + 30)/(10)`

Calculate 53+30

`\sf \: y = (83)/(10)`

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