Question 665239
Establish variables
x = larger number
y = smaller number
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Given
x = 7+3y
{{{highlight_green(x-y = 61)}}}
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Substitute x into the second equation
7+3y - y = 61
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Combine like terms
3y-y = 61 - 7
2y = 54
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Divide both sides by 2
{{{highlight(y = 27)}}} as the smaller number
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Rearrange x = 7+3y to y = {{{(x-7)/3}}}
Substitute into the equation and solve for x
x - {{{(x-7)/3}}} = 61
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Multiply the equation by 3 to be rid of the fraction
3x - (x-7) = 183
3x - x + 7 = 183
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Combine like terms
3x - x = 183-7
2x = 176
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Divide both sides by 2
{{{highlight(x = 88)}}} as the larger number
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Numbers are {{{highlight(88)}}} and {{{highlight(27)}}}
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Check {{{cartoon(
88 - 27, 61)}}}
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