Question Video: Solving a System of Two Linear Equations Simultaneously Mathematics • 8th Grade

Solve the simultaneous equations π₯ β π¦ = 4 and π₯ + π¦ = 14.

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Video Transcript

Solve the simultaneous equations π₯ minus π¦ equals four and π₯ plus π¦ equals 14.

We have these two equations, and theyβre in a pretty similar format. One of them is saying π₯ minus π¦ equals something, and the other one is saying π₯ plus π¦ equals something.

To solve this equation, weβre going to use a process called the elimination. Weβ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 π¦ plus π¦ equals zero. Those cancel out. And last, weβ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 π¦. Iβm going to use the second equation. The reason for that is Iβm adding π₯ plus π¦.

In the first equation, we have a negative π¦, so we would still be able to solve for π¦ in this case, but it would take a few more extra steps. So letβs use π₯ plus π¦ equals 14. We want to plug in nine for the π₯ value, to say nine plus π¦ equals 14, but remember weβre trying to find out what π¦ is.

To isolate π¦, weβll subtract nine from both sides of the equation. By taking nine away from the left side of the equation, weβre left with only π¦. Subtracting nine from 14 gives us five. Our π¦-coordinate will be equal to five; π₯ equals nine; π¦ equals five.