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Video: Solving a System of Two Linear Equations Simultaneously

Kathryn Kingham

Solve the simultaneous equations 𝑥 βˆ’ 𝑦 = 4 and 𝑥 + 𝑦 = 14.

02:27

Video Transcript

Solve the simultaneous equations π‘₯ minus 𝑦 equals four and π‘₯ plus 𝑦 equals 14.

We have these two equations, and they’re in a pretty similar format. One of them is saying π‘₯ minus 𝑦 equals something, and the other one is saying π‘₯ 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 π‘₯ plus π‘₯ equals two π‘₯. Then we can say negative 𝑦 plus 𝑦 equals zero. Those cancel out. And last, we’ll add four plus 14 equals 18.

We now know that two π‘₯ equals 18, and we can solve for π‘₯. We divide both sides of the equation by two to get π‘₯ by itself. Two π‘₯ divided by two equals π‘₯; 18 divided by two equals nine, so we know that our π‘₯ 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 π‘₯ 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 π‘₯ plus 𝑦 equals 14. We want to plug in nine for the π‘₯ 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; π‘₯ equals nine; 𝑦 equals five.