how to solve this problem by substitution 3x+y=4 y=4x-3

Question

I'm not getting it

Answer 1

Hi Jamie!

 

Since you have two variables, you must substitute to have one variable to solve.

 

3x+y=4

y=4x-3

 

3x+(4x-3)=4

 

3x+4x-3=4

 

7x-3=4

 

7x=7

 

x=1 *Now to solve for y, we can plug in the value of x

 

y=4(1)-3

 

y=4-3

 

y=1

Answer 2

3x + y = 4

y = 4x - 3

 

Since y= 4x+3, substitute 4x+3 in place of the y in the first equation:

 

3x + y = 4

3x + (4x-3) = 4      [Substituted 4x-3 in place of y]

3x + 4x - 3 = 4

7x = 7

x = 1

 

T0 find y use the second equation and the fact that x = 1:

 

y = 4x - 3

y = 4(1) - 3

y = 1

 

Check:

3x + y = 4

3(1) + 1 = 4

4 = 4

Check!

y = 4x - 3

1 = 4(1) - 3

1 = 1

Check!

Answer 3

TO begin solving by substitution you'll need to find an expression for one variable in terms of the other variable. In this case you are given an expression for y in terms of x:

 

y = 4x -3

 

This equation allows you to substitute the variable y with (4x-3). You can do thins in the first given equation:

 

3x + y = 4 

⇒ 3x + (4x - 3) = 4

 

Grouping like terms 

 

7x -3 = 4

 

Then adding 3 on both sides:

 

7x = 7

 

And dividing by 7 on both sides:

 

x = 1

 

Since you now know the value for x, 1, you can plug in 1 for x in the given equation:

 

y = 4x - 3

⇒ y = 4 × 1 - 3

      = 4 - 3

      = 1

 

Meaning that the solution is: x = 1 and y = 1.