SOLUTION: I need help immediately :( I don't understand these equations , I was absent. I'm crying :(( I can't do all of these. [ Substitution ] y=3x-4 y= -5x + 4 y=2x+13 y=-

Question 598406: I need help immediately :(
I don't understand these equations , I was absent.
I'm crying :(( I can't do all of these.
[ Substitution ]
y=3x-4
y= -5x + 4

y=2x+13
y=-4x-23

y=3x+20
y=x+4

y=-4x-8
y=3x+13

------
-x+y=6
y=-7+14

y=-5x+12
x+y=-3

x+y=-6
y=-3x-10

-4x+5y=-15
4x+y=21
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The basic idea is to replace one variable with another expression (of that other variable) so you can eliminate one variable.

This way, you'll have a single equation with one variable. You then solve that equation to find the value of that variable. Then you use the solution to find the value of the previously eliminated variable.
=======================================================
# 1
y=3x-4
y= -5x + 4

y=3x-4
-5x+4=3x-4 ... Note: I'm replacing the 'y' with -5x+4 (since y = -5x+4)
-5x-3x=-4-4
-8x=-8
x=-8/(-8)
x = 1
-------------
y = 3x-4
y = 3(1)-4 ... Here I'm replacing 'x' with 1 (since x = 1)
y = 3-4
y = -1

So x = 1 and y = -1

=======================================================
# 2
y=2x+13
y=-4x-23

y=2x+13
-4x-23=2x+13
-4x-2x=13+23
-6x=36
x=36/(-6)
x = -6
--------------
y = 2x+13
y = 2(-6)+13
y = -12+13
y = 1
So x = -6 and y = 1
=======================================================
# 3
y=3x+20
y=x+4

y=3x+20
x+4=3x+20
x-3x=20-4
-2x=16
x=16/(-2)
x = -8
----------------
y = 3x+20
y = 3(-8)+20
y = -24+20
y = -4

So x = -8 and y = -4

=======================================================
# 4
y=-4x-8
y=3x+13

y=-4x-8
3x+13=-4x-8
3x+4x=-8-13
7x=-21
x=-21/7
x=-3
-----------------
y = -4x-8
y = -4(-3)-8
y = 12-8
y = 4

So x = -3 and y = 4

=======================================================
# 5
-x+y=6
y=-7+14

There's a typo in the second equation. Please repost this one. Thanks
=======================================================
# 6
y=-5x+12
x+y=-3

x+y=-3
x+(-5x+12)=-3
x-5x+12=-3
x-5x=-3-12
-4x=-15
x=-15/(-4)
x=15/4
----------------
y = -5x+12
y = -5(15/4)+12
y = -75/4+12
y = -75/4+48/4
y = -27/4

So x = 15/4 and y = -27/4
=======================================================
# 7
x+y=-6
y=-3x-10

x+y=-6
x+(-3x-10)=-6
x-3x-10=-6
x-3x=-6+10
-2x=4
x=4/(-2)
x = -2
------------------
y = -3x-10
y = -3(-2)-10
y = 6-10
y = -4

So x = -2 and y = -4
=======================================================
# 8
-4x+5y=-15
4x+y=21

First we need to solve one equation for one variable. I'm going to solve the second equation for y.

4x+y=21
y=21-4x
y = -4x+21
-----------
Now use substitution to solve

-4x+5y=-15
-4x+5(-4x+21)=-15
-4x-20x+105=-15
-4x-20x=-15-105
-24x=-120
x=-120/(-24)
x = 5
-----------
y = -4x+21
y = -4(5)+21
y = -20+21
y = 1

So x = 5 and y = 1
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