# Algebra 1

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Substitution

x - 5y=10
2x - 10y=20

• Algebra 1 -

The equations are the same (divide the second equation by 2). There is no solution.

• Algebra 1 -

to do substitution: you choose one equation, then represent one of the variables in terms in terms of the other. and finally substitute it the the other equation.

(1) x - 5y = 10
(2) 2x - 10y = 20

here, let's choose equation (1), and let's represent x in terms of variable y:
x - 5y = 10
x = 5y + 10
then we substitute this to equation (2):
2x - 10y = 20
2(5y + 10) - 10y = 20
10y + 20 - 10y = 20
20 = 20

note that when you come with this answer (constant = constant), this means that the lines are coinciding, meaning any point can be a solution, because the equations are "equal". if you observe equation (2), we can factor out 2:
2x - 10y = 20
2(x - 5y) = 2(10)
x - 5y = 10
it becomes equation (1).

hope this helps~ :)

• Algebra 1 -

X+4y=8
2x-5y=29

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