Question

solve the system by the substitution method.

X+Y=4
Y=3x

Answer 1

how do you think we should go about this?

Answer 2

substitution is usually quite labor intensive; but they gave you an easy one to give you the feel for it and build your confidence

Answer 3

If they tell you outright that Y = some value; then wherever you encounter a Y; "substitute" that value in for it and solve

Answer 4

so, x+3x=4?

Answer 5

thats correct; now we solve for X to get a good solid value that we can use

Answer 6

x+3x = 4
x(1+3) = 4
x(4) = 4
x = 4/4

x=1

since x=1 we know what y has to equal as well because they tell us that y = 3x

y = 3(1)
y= 3

Answer 7

thank you!

Answer 8

so, i have a similar question i need help with--
if x+3y=8 and y=2x-9 then the equation would be x+3(2x-9)=8?

Answer 9

let me see

x+3y = 8
y = 2x-9 ; sub this value in the top

x+3(2x-9) = 8 ; and work it thru to solve for x, thats right

then use your solid value for x to determine a solid value for y

Answer 10

x+6x-9=8
x(1+6)-9=8
7x-9=8
7x=8+9
7x=17
x=17/7?

Answer 11

you missed it up top; x +6x -27 = 8 :) the rest looks like good form tho

Answer 12

in other words you 9*2 off

17
18
---
35 so 35/7 = 5

Answer 13

to work it out

x+3(2x-9) = 8
x+3(2x)-3(9) = 8
x +6x -27 = 8
x(1+6) -27 = 8
x(7) -27 = 8
x(7) = 8 + 27
x = 35/7
x = 5 :)

Answer 14

right! was trying to do mental math. got it! i'm also confused with x+3y=5
4x+5y=13
do i combine like terms?

Answer 15

x=5-3y
4(5-3y)+5y=13
20-12y+5y=13
20-7y=13
-7y=-7
y=1

x=5-3(1)
x=2

Answer 16

subbing is time consuming and take alot of unneeded mathing; the next step they teach you will be "elimination" whcih takes advantage of the fact the equations can change shape and still keep the same value; kinda like fractions. Just remember that what you do to one side has to be done to it all ....

x+3y = 5 ; spose we multiply this one by -4 what do we get?
4x+5y = 13

x +3y = 5
-4
------------
-4x-12y =-20 ; this new equation has the same inherent value as
the one it came from, weve only change the shape
of it.

Now we have something useful to us that we can use to "eliminate" one of the variables with ... watch.

-4x-12y=-20 <-- our reshaped equation
4x+5y = 13
------------ ; and add them together
0x -7y =-7 <--- now this is easily worked out for y

-7y = -7
y = -7/-7
y = 1

Answer 17

and since y = 1; use it in any of the equation to get the value for x

x +3y = 5
x +3(1) = 5
x + 3 = 5
x = 5-3
x = 2