Question

How do you solve `x+2y=3` and `3x-y= -5`?

Answer 1

`color(red)(x=-1, y=2)`

Explanation:

One way is to use the method of substitution.

Step 1. Enter the equations.

[1] `x+2y=3`
[2] `3x-y=-5`

Step 2. Solve for one variable in terms of the other.

Solve Equation 2 for `y`.

[3] `y=3x+5`

Step 3. Substitute Equation 3 in Equation 1 and solve for `x`.

`x+2(3x+5)=3`

`x+6x+10=3`

`7x=-7`

[4] `x=-1`

Step 4. Substitute Equation 4 in Equation 1:

`-1+2y=3`

`2y=4`

`y=2`

The solution is `x=-1, y=2`.

Check:

Substitute the values in Equation 2.

`3x-y=-5`

`3(-1)-2=-5`

`-3-2=-5`

`5=5`

It works!