Solve the system of equations using the substitution method?

step 1; 3x+ y= 7
4x- y=21
cancel +y and -y
3x=7
4x=21
add 4x and 3x , and 7 and 21
7x= 28
7x/7= 28/7
x= 4

step 2; choose one equation

3(4)+ y= 7
12 + y=7
y= 7-12
y= -5

step 3; substitute
3(4) + -5= 7
12-5=7
7=7 correct!!!!

4(4) - -5=21
16+5=21
21=21 correct!!!!!

y = 7 - 3x

4x - (7 - 3x) = 21

7x - 7 = 21

7x = 28

x = 4

12 + y = 7

y = - 5

x = 4 , y = - 5

y=-3x+7

4x-(-3x+7)=21
4x+3x-7=21
7x-7=21
7x=28
x=4

3(4)-y=7
12-y=7
y=5

3x + y = 7
4x - y = 21

3x + y = 7
y = 7 - 3x

4x - y = 21
4x - (7 - 3x) = 21
4x - 7 + 3x = 21
4x + 3x = 21 + 7
7x = 28
x = 28/7
x = 4

4x - y = 21
4(4) - y = 21
-y = 21 - 16
-y = 5
y = 5/-1
y = -5

∴ x = 4 , y = -5 (4,-5)

3x + y = 7 Eq. (1)
4x – y = 21 Eq. (2)
Solve by substitution.
From Eq. (1)
y = 7 - 3x
Substitute into Eq. (2)
4x - (7 - 3x) = 21
4 - 7 + 3x = 21
7x = 28
x = 28/7 = 4
y = 7 - 3(4) = -5
(x, y) = (4, -5)

Happy Holidays!

x = 4
y = -5

3x + y = 7
Subtract 3x from both sides giving y = -3x + 7
Now substitute this into the other equation for y, giving you
4x - (-3x + 7) = 21
Distribute the minus through the parenthesis.
4x + 3x -7 = 21
Now add 7 to both sides and combine the x terms
7x = 28, divide both sides by 7.
x = 4.

Now plug 4 in for x in either of the original equations
3(4) + y = 7
Subtract 12 from both sides
y = -5

or

4 (4) - y = 21
Add y to both sides and subtract 21
y = -5

Enjoy!

The substitution method is as follows:
3x+y=7 (1)
4x-y=21 (2)
Now, take equation (1) and solve for y (get y on one side):
y=7-3x (3)
This formula has just established a value of y for formula (1).
Now, plug this value into formula (2)
4x - [7-3x]=21
Now open the parenthesis, remembering to distribute the negative.
4x-7+3x=21
Add 4x and 3x.
7x-7=21
Add 7 to both sides
7x=28
divide by 7
x=4
Plug that value of x into formula (1)
3(*4)+y=7
12+y=7
y=7-12
y=-5.
So you see that x = 4 and y = -5, hence (4,-5)
Glad I could help! =D