Solve the system of equations using the substitution method.?

Hi,

3x + y = 7

4x – y = 21

Solve the first equation for y. Substitute this expression into the second equation for y and solve.

y = 7 - 3x

4x - (7 - 3x) = 21

4x - 7 + 3x = 21

7x - 7 = 21

7x = 28

x = 4

If x = 4 and y = 7 - 3x, then y = -5.

(4,-5) <==ANSWER

I hope that helps!! :-)

3x + y = 7

4x - y = 21

To solve this using substitution, you must express one variable in terms of the other in one of the equations, and plug into the other equation.

From the first equation, since 3x + y = 7, it follows that

y = 7 - 3x

So all we have to do is plug this into the second equation, 4x - y = 21, to get

4x - (7 - 3x) = 21

Now, solve for x.

4x - 7 + 3x = 21

7x - 7 = 21

7x = 28

x = 4

Now that we have x = 4, it is easy to get y. Just plug in x = 4 into any one of the two equations. Let's use 3x + y = 7.

3(4) + y = 7

12 + y = 7

y = -5

So x = 4, y = -5, and the answer as an ordered pair is

(4, -5)

From the bottom equation, y = 4x - 21

Substitute this value in eq 1 above.

3x + (4x - 21) = 7

7x = 28

x = 4

With x = 4 then y = -5

3x + y = 7

4x – y = 21

from 2nd equation y = 4x - 21

substituting this into eqn 1

3x +4x -21 = 7

7x = 28

x = 4

12 + y = 7

y = -5

(4, -5)