I don't get it???

Question

solve the system by substitution.

3x+2y=17
y=-2x+12

I don't understand what to substitute???

Answer 1

substitution means to put in whatever Y equals to (which is in terms of x) into the Y of another equation. by doing this, you are eliminating the Y in that equation and are left with just x and values, which you can then work out.

In this case,

y=-2x+12

so put the -2x + 12 into the next equation: 3x+2y=17

so...

3x + 2 (y) =17
3x + 2 (-2x +12) =17

Notice that whether i say Y or (-2x +12 ) it doesn't matter because they are equal? Thats why i can put -2x +12 in place of Y and get the my first equation all in x and values

so now i'm left with
3x + 2 (-2x +12) =17

Open it up.

3x - 4x +24 =17
-x +24=17
-x= 17-24
-x= -7
x=7

so now that x = 7,

just put back into the first equation
3x+2y=17

3(7)+ 2y= 17
21+2y= 17
2y= 17-21
2y= -4
y=-2

Answer 2

call
3X + 2Y = 17 .......equation (1)
and
Y = -2X +12 ...........equation (2)

Substitute Y = -2X + 12 for Y in (1)

you have

3X + 2(-2X+12) = 17

Multiply the values in the parentheses with the 2 outside the parentheses

3X -4X + 24 = 17

Put like terms together

3X - 4X = 17 -24
-X = -7

you have negative X, you need value of positive X, multiply through out the above equation with -

X = 7

When you solve a set of equations, you have the values of both the variables(X and Y), you have X now. To get the value of Y, substitute the value of X = 7 in eq(2).
You have Y = -2

so the solution is X = 7, Y = -2

Answer 3

One of the variables (y) is already defined in terms of the other variable:
y=-2x + 12

So substitute that value for y in the other equation:

3x +2(-2x + 12) = 17

Then solve for x:

3x + -4X + 24 = 17
-x + 24 = 17
-x = -7
x = 7

Answer 4

3x+2y=17
y=-2x+12 insert the Y in the bottom equation with the Y in top
equation liek so:
3x+2(-2x+12)=17 now distribute and multiply the 2 in 2(-2x+12)
2 X -2x=-4x and 2 X 12=24 now you get this:
3x+-4x+24=17 now add the numbers WITH x ( 3x+-4x)
3x+-4x=-1x now you get:
-1x+24=17 now SUBTRACT the numbers WITHOUT x (24 - 17)
24-17 or how i was taught 24+-17(the same in MOST situations)
this one we can ust subtract(use your calculator to
determine if there is a diff answer if you change the
signs around, if theyre is, go with the n=-n=n one
so, 24-17=-7 now you have:
-1x=-7 now divide to get your final answer! like so
-7 divided by -1x which equals 7x which is your final answer!!

how it should kinda look when workign them out:
3x+2y=17
y=-2x=12
3x+2(-2x+12)=17
3x+-4x + 24=17
3x+-4x=-1x
-1x+24=17
24-17=-7
-1x=-7
7divided by -1x = 7x

hope this helped...im not very good at explaining things, sorry...good luck

Answer 5

3x + 2(-2x+12) = 17
3x -4x + 24 = 17
-x + 24 =17
24-17 = x
7 = x

y = -2(7) + 12
y = -14 + 12
y = -2

3(7) + 2(-2) = 17
21 - 4 = 17
17 = 17

Answer 6

i'm learning the same math as you are.. =)

you see y=-2x+12. you subsitute to the first equation

equation: 3x+2y=17
subsitute: 3x+2(-2x+12)=17.
then you solve by distribution: 2(-2x+12) is the same as -4x+24 and so on.. good luck!

3x-4x+24=17
3x-4x=(-x) & add -24 to 17=7
-x=7
divide (neg) to both side
x=7

Answer 7

3x+2(-2x+12)=17
then distribute equation in parenthesis:
3x+-4x+24=17
then combine like terms:
7x=-7
then divide:
x=-1


To find Y, simply plug in X in your equation:
3x+2y=17
3(-1)+2y=17
-3+2y=17
then add 3 to both sides
2y=20
y=10


To check your solutions, plug x and y into equation
3(-1)+2(10)=17
-3+20=17
17=17

Answer 8

In the first equation (3x+2y=17), replace the 'y' with the second equation, since you know what 'y' equals in terms of 'x'. Then expand the equation and solve.

Answer 9

3x+2(-2x+12)=17
3x-4x-24
-1x-24=17
x=-41

To Check:

3(-41)+2(-2(-41)+12))=17
-123+164-24=17
17=17

Answer 10

The 1st eq is
3x+2y+17.............(1)
Rewrite 2nd eq as
2x+y=12 (2)

Multiply (2) by 2:
4x+2y=24..............(3).

(3)-(1) gives
x=7.
Substitute in (1) or (2)
to get y.