Solve the simultaneous equations 𝑥 minus 𝑦 equals four and 𝑥 plus 𝑦 equals
We have these two equations, and they’re in a pretty similar format. One of them is saying 𝑥 minus
𝑦 equals something, and the other one is saying 𝑥 plus 𝑦 equals something.
To solve this equation, we’re going to use a process called the elimination. We’re actually going to add both
of these equations together. For our first line, we say 𝑥 plus 𝑥 equals two 𝑥. Then we can say
negative 𝑦 plus 𝑦 equals zero. Those cancel out. And last, we’ll add four plus 14 equals
We now know that two 𝑥 equals 18, and we can solve for 𝑥. We divide both sides of
the equation by two to get 𝑥 by itself. Two 𝑥 divided by two equals 𝑥; 18 divided by two
equals nine, so we know that our 𝑥 equals nine.
After that, we can take this information that we were
given and plug it in to one of the equations to solve for 𝑦. I’m going to use the second
equation. The reason for that is I’m adding 𝑥 plus 𝑦.
In the first equation, we have a negative
𝑦, so we would still be able to solve for 𝑦 in this case, but it would take a few more extra
steps. So let’s use 𝑥 plus 𝑦 equals 14. We want to plug in nine for the 𝑥 value, to say
nine plus 𝑦 equals 14, but remember we’re trying to find out what 𝑦 is.
To isolate 𝑦, we’ll
subtract nine from both sides of the equation. By taking nine away from the left side of the
equation, we’re left with only 𝑦. Subtracting nine from 14 gives us five. Our 𝑦-coordinate
will be equal to five; 𝑥 equals nine; 𝑦 equals five.