Solve the simultaneous equations, 𝑥 minus 𝑦 equals eight and three 𝑥 minus five 𝑦 plus ten equals zero.
We can begin by taking one of these equations and isolating a variable. Let’s go ahead and take 𝑥 minus 𝑦 equals eight, since it’s smaller. And what we’ll do, is we’ll solve for 𝑥. So let’s add 𝑦 to both sides of the equation, which means 𝑥 is equal to 𝑦 plus eight. So what we can do now is we can take this 𝑥 equals 𝑦 plus eight and plug that in for 𝑥 into the other equation. So we’ll take this equation and we’ll substitute 𝑦 plus eight in for 𝑥.
Now we can use the distributive property. Now that we’ve taken three times 𝑦 to get three 𝑦 and three times eight to get twenty-four, we can combine like terms. We have three 𝑦 and negative five 𝑦 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, 𝑦 is equal to seventeen. Now that we have a value for 𝑦, we can plug it in and solve for 𝑥. So 𝑥 is equal to seventeen plus eight, which is twenty-five. Therefore again, 𝑥 is equal to twenty-five and 𝑦 is equal to seventeen.