Question

How do you solve the system of equations `3x+y=1` and `y+4=5x` using substitution?

Answer 1

The solution is `x=5/8, y=-7/8`.

The key to solving by substitution is to rearrange an equation to get an expression for one variable in terms of the other, and to then substitute that value into the second equation.

Explanation:

There are a number of possible approaches, but here's one.

Call this Equation 1:

`3x+y=1`

And this Equation 2:

`y+4=5x`

Let's rearrange Equation 2 to make `y` the subject (by subtracting 4 from both sides):

`y=5x-4`

Now we have a value for `y` in terms of `x`. We can substitute that for `y` in Equation 1:

`3x+(5x-4)=1`

This is an equation in only one variable, `x`, so we can solve it.

`3x+5x-4=1`

`8x=5`

`x=5/8`

We can substitute this value into either Equation 1 or Equation 2 and solve for `y`. I'll choose Equation 1:

`3(5/8)+y=1`

`15/8+y=1`

`y=1-15/8=-7/8`