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!!!!!

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)

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

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!

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!

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

x = 4

y = -5