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