# math

posted by .

solve by substitution
1. y = x - 3
x + y = 5

2. 5x + 2y = 0
x - 3y =0

• math -

if y=x-3, then you have to plug it into the equation.
for numb 1, y=x-3 so when you plug that in it makes the equation x+y=5 turns into x+x-3=5. then you solve by making the sides equal.

you do this by x+x-3=5
x-3=3
x=2

• math -

I'm with Zava on the idea, but I think one of us dropped a sign along the way. And I'm not at all sure it wasn't me, so I'll check at the end. Dropped signs happen all the time.

We have:

x + y = 5

but we're also given what y is: y = x - 3

So we can just replace y in the equation with (x-3)

x + y = 5

x + (x-3) = 5

2x - 3 = 5

2x = 5 + 3

2x = 8

x = 4

and since y = x -3

y = 4 - 3 = 1

Check:

y = x - 3
1 = 4 - 3 - OK

x + y = 5
4 + 1 = 5 - OK

The second one is a leetle trickiersince you''ll have to make one of the equations work for the substitution

x - 3y = 0

-> x = 3y --- that's the one we'll use!

5x + 2y = 0

5(3y) + 2y = 0

17y = 0 -> y = 0.

No that's not a mistake. The only answer is if x and y are both zero!

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