Video Transcript
Solve the simultaneous equations, ๐ฅ minus ๐ฆ equals eight and three ๐ฅ minus five ๐ฆ plus ten equals zero.
We can begin by taking one of these equations and isolating a variable. Letโs go ahead and take ๐ฅ minus ๐ฆ equals eight, since itโs smaller. And what weโll do, is weโll solve for ๐ฅ. So letโs add ๐ฆ to both sides of the equation, which means ๐ฅ is equal to ๐ฆ plus eight. So what we can do now is we can take this ๐ฅ equals ๐ฆ plus eight and plug that in for ๐ฅ into the other equation. So weโll take this equation and weโll substitute ๐ฆ plus eight in for ๐ฅ.
Now we can use the distributive property. Now that weโve taken three times ๐ฆ to get three ๐ฆ and three times eight to get twenty-four, we can combine like terms. We have three ๐ฆ and negative five ๐ฆ we can combine, and twenty-four and ten we can combine. Now we need to subtract thirty-four from both sides. And lastly, divide both sides by negative two.
Therefore, ๐ฆ is equal to seventeen. Now that we have a value for ๐ฆ, we can plug it in and solve for ๐ฅ. So ๐ฅ is equal to seventeen plus eight, which is twenty-five. Therefore again, ๐ฅ is equal to twenty-five and ๐ฆ is equal to seventeen.