Substition Method...?

Question

Solve by Sustitution Method: Determine if the equations are independent, dependent, or inconsistent!

x = y +3
3x - 2y = 4

I would appreciate it if someone can show me the steps as best as possible. Thank you..so much!

Answer 1

Plug the first equation into the second equation:
3(y + 3) - 2y = 4

Distribute the 3:
3y + 9 - 2y = 4

Combine terms:
y = -5

Plug that value back into the first equation:
x = -5 + 3
x = -2

Answer 2

3x - 2y = 4
3(y + 3) - 2y = 4
3y + 9 - 2y = 4
y + 9 = 4
y = -5

x = -5 + 3
x = -2

These equations are not inconsistant, because there is a specific solution for x and y that satisfies both equations. They are not independant because they can be solved. I believe this would mean they are independant.

Answer 3

x = (y+3)

3(y+3) - 2 y = 4

(Notice I substituted y+3 in for x in the second equation.)

Now you have an equation with one variable, solve for y.

3y+9-2y = 4
y+9 = 4
y = -5

x = -5 + 3 = -2

The equations are independent.

Answer 4

x= y+3
3x - 2y=4

you simply replace the x in the second equation with y+3, so...

3(y+3) -2y=4
3y + 9 - 2y =4
3y-2y=4-9
1y=-5
y=-5

so then if y=-5, substitute that into the first or second equation again.
x=y+3
x=-5+3
x=-2

now check it with the other problem
3x-2y=4
3(-2) -2(-5)=4
-6 - -10=4

x= -2, y=-5

Answer 5

first u substitute the x=y+3 into the 2nd equation so it reads,
3(y+3)-2y=4. now that u have only vairable in the ewaution u cna go ahead and solve it to get y=1. then plug in 1 for y into any of the original equations to solve for x. you should get x=4.