SOLUTION: solve using the substituion method. #1 y=6-x 2x-3y=22 #2 x+2y=5 x+y=2 #3 x+y=31 x-y=17 #4 7x+y=10 2y+5x=11

Question 4999: solve using the substituion method.
#1
y=6-x
2x-3y=22

#2
x+2y=5
x+y=2

#3
x+y=31
x-y=17

#4
7x+y=10
2y+5x=11

Answer by lotanez(23) (Show Source): You can put this solution on YOUR website!
Solve for one value in the first equation and then substitute this value in the second equation. Then enter the answer to the orginal equation.
#1. y = 6 - x
2x - 3y = 22
2x - 3(6-x) = 22
2x - 18 - 3x = 22
2x - 18 + 18 - 3x = 22 + 18
2x - 3x = 40
-1x = 40
-1x/-1 = 40/- 1
x = -40
y = 6 - 40
y = -34
Check: enter in the x and y values into the orginal equation:
-34 = 6 -40
-34 = -34
#2. x + 2y = 5
x + y = 2: x - x + y = 2 - x; y = 2 - x (rewrite equation)
(fill in the y = 2 - x into the first equation)
x + 2(2 - x) = 5
x + 4 - 2x = 5
x + 4 - 4 - 2x = 5 - 4
x - 2x = 1
-x = 1
x = -1
x + y = 2
-1 + y = 2
-1 + 1 + y = 2 + 1
y = 3
Check:
-1 + 2(3) = 5
-1 + 6 = 5
5 = 5
#3. x + y = 31
x - y = 17
x = 31 - y
31 - y - y = 17
31 - 31 - 2y = 17 - 31
-2y = -14
-2y/-2 = -14/-2
y = 7
x + y = 31
x + 7 = 31
x + 7 - 7 = 31 - 7
x = 24
Check:
24 + 7 = 31
31 = 31
#4. 7x + y = 10: y = -7x + 10
2y + 5x = 11
2(-7x + 10) + 5x = 11
-14x + 20 + 5x = 11
-14x + 20 - 20 + 5x = 11 - 20
-14x + 5x = -9
-9x = -9
-9x/-9 = -9/-9
x = -1
7x + y = 10
7(-1) + y = 10
-7 + y = 1
7 - 7 + y = 10 - 7
y = -3
Check:
2(-3) + 5(-1) = 11
-6 + -5 = 11
Check:
7(1) + -6 = 10

RELATED QUESTIONS
If anyone could please help me to solve these four problems it would be awesome! I am... (answered by Alan3354)

If anyone could please help me to solve these four problems it would be awesome! I am... (answered by stanbon)

how do you solve 1-5 using the substitution method. 1. 4x+3y=11 x=3y-1 2. 2x+3y=5 (answered by unlockmath)

1. 4x+3y=1, x=1-y 2. 2x-y=6, -x+y=-1 3. 6x-y=3, 4x-2y=-2 4. 2x+3y=7, x=1-4y 5.... (answered by AnlytcPhil)

SOLVE STEP BY STEP THANK YOU:) 1) x+y=5 3x-y=7 2) 2x+y=3 -2x+5y=-9 3) 3x+5y=0 (answered by Alan3354)

Solve the following systems of linear equation by using Substitution Method: 1,) X +3y (answered by josgarithmetic)

Solve the system using the substitution method. Show all your steps. 1. x+2y=6... (answered by checkley79)

1) x+y=9 x+2y=13 x= y= 2) 3x+7y= 24 9x+5y=24 x= y= 3) 4x+y=17 2x+3y+21 x= (answered by Fombitz)

Have I correctly solved the 4 problems below using the systems of simultaneous equations, (answered by ikleyn)