Question

How do you solve this system of equations: `7p + 8q = 11 and 3p + 4q = 3`?

Answer 1

`p=5\quad,\quad q=-3`

Explanation:

We can use elimination to solve this.

Let’s try to eliminate `q`, to solve for `p` first:

`7p+8q=11`

`3p+4q=3`

Multiply both sides of the bottom equation by `-2`:

`-2(3p+4q)=(3)-2`

`\rightarrow -6p-8q=-6`

Now, the `q` terms in both equations are opposites of each other, so they will cancel out and give us the value of `p`.

To do that, we need to add both equations together:

`(-6p-8q=-6)\quad +\quad (7p+8q=1)`

`\rightarrow p=5`

Knowing that, we can plug the value of `p` into one of the equations to find the value of `q`:

`7p+8q=11`

`\rightarrow 7(5)+8q=11`

`\rightarrow 35+8q=11`

`\rightarrow 8q=-24`

`\rightarrow q=-3`

---

Now that we have the values of both variables, we can plug them into one of the equations to check our work:

`3p+4q=3`

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

`15-12=3`

`3=3`

So it’s right.