Solve the system of equations using the substitution method.?

Solving first equation for y:

y = 7 - 3x

Substituting for y in the second equation:

4x - (7 - 3x) = 21

4x - 7 + 3x = 21

4x + 3x = 21 + 7

7x = 28

x = 28/7

x = 4

Substituting this answer for x back into the first equation:

3(4) + y = 7

y = 7 - 12

y = -5

Now, to double check, lets use the second equation:

4(4) - (-5) = 21

16 + 5 = 21

Check!

It is a unique solution, so ordered pair representation would be (4, -5).

Some people used elimination. In substitution, solve for a variable (in either equation). Substitute the solution for tthe varialbe in the other equation, and solve. Then substitute that solution into either equation and solve.

Here the easy way is to solve for y in the 1st. Subs. 7-3x for y in the 2nd, solve for x giving x=4, and replace x with 4 in either equation to solve for y. y=-5

It's B. I did it on my graphing calculator but here's the paper way to do it; X + 2(x+3) = 12 X + 2x + 6 = 12 Subtract 6 and add the x's 3X = 6 Divide by 3 X=2 Y=(2)+3 Y=5 (2,5) Hope that helped ^^

Add the 2 equations together, the y terms will cancel and disappear, giving

7x = 28, so x is 4

Then substituting x=4 into either of the original equations (may as well choose the first):

12 + y = 7

so y must be -5

3x + y = 7 Eq. (1)

4x – y = 21 Eq. (2)

From Eq. (1) solve for y

y = 7 - 3x

Subtitute in Eq. (2)

4x - (7 - 3x) = 21

4x - 7 + 3x = 21

7x = 28

x = 4

y = 7 - 3(4) = -5

(x, y) = (4, -5)

3x=y=7

now subtract 3x

y=-3x+7

substitute for y in next equation

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

and solve!

3x + y = 7.................1

4x – y = 21................2

multpyl 1x4 and 2x3

12x+4y=28

12x-3y=63

.......................subtraction

7y=-35

y=-35/7=-5

3x+(-5)=7

3x=7+5

3x=12

x=12/3=4

the solution(4,-5)