Question

How do you find the solution of the system of equations `3x+4y=10` and `x-y=1`?

Answer 1

`x=2` and `y=1`

Explanation:

For such a simple system, you can use substitution: `x=y+1` from the second equation. Substitute this value of `x` in the first equation to the effect that
`3(y+1)+4y=10`. this simplifies to `7y=7`, that is `y=1`.

Substitute back in the second equation to get `x=y+1=1+1=2`.

Answer 2

`x=2,y=1`

Explanation:

The key insight here is that for the second equation, we can easily solve for a variable in term of the other variable.

Let's just add `y` to both sides to solve for `x` in terms of `y`. We get

`color(blue)(x=y+1)`

We can plug this value of `x` into the first equation in the system. We get

`3(y+1)+4y=10`

Distributing the `3` to both terms in the parenthesis, we get

`3y+3+4y=10`

Combining like terms, we now have

`7y+3=10`

Subtracting `3` from both sides, we get

`7y=7`

Dividing both sides by `7`, we find that

`color(red)(y=1)`

We can plug this value into the blue expression to get

`x=1+1`

`color(red)(=>x=2)`

Hope this helps!