substitution please explain answer

Question

{y=2x+3

{y=4x-1

Answer 1

The problem gives us two equations.  To "solve" them means to find the values for x and y for which they are both true.

 

One method for solving this system of equations is called Substitution.  That means that we get an expression for one variable using one equation and then substitute it into each place the variable occurs in the other equation.  We could solve for either x or y using either equation, but let's use the second equation (notice that it already has an expression for y) and substitute that in place of the y in the first equation.

          y    = 2x + 3

      (4x-1) = 2x + 3

        2x - 1 = 3             [subtract 2x from both sides]

         2x = 4                 [add 1 to both sides]

          x = 2                 [divide both sides by 2]

 

Now, substitute (there's that word again) this value of y into either equation (which one is easier?):

       y = 2(2) + 3

       y = 7

Answer 2

Since both equations are equal to y we can set them equal to each other.

2x+3=4x-1

4=2x

x=2

 

Then plug x into equation to find y

y=2(2)+3

y=7

 

 

You could also solve for x in one equation and plug that into the other

y=2x+3 is the same as x=(y-3)/2

so you can now plug this into the other equations to obtain

y=4((y-3)/2)-1 but this example is a bit more complicated that way. 

 

 

Another way to do it (elimination)!

First you need to determine a variable to eliminate. Here if we multiply the first equation by -2 we obtain:

-2y=-4x-6

y=4x-1

 

After adding these equations we get

-y=-7; so y=7

 

plugging this into one of the original equations we can find x.

7=4x-1

8=4x

x=2

 

Either way we got the same answer! Hope this helped.

Answer 3

Since 2x+3 and 4x-1 both equal to y,

we can let 2x+3=4x-1 and slove for x.

-2x =-4

x=2

plug back to the first equation to get y:

y=2*2+3=7

So x=2, y=7