Question 298382
Set-Up
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Equation 1: {{{A = B + 7}}}
Equation 2: {{{A^2 + B^2 = 29}}}

Solution:
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Plug (B+7) into equation 2 for A
Equation 2: {{{A^2 + B^2 = 29}}}
{{{(B + 7)^2 + B^2 = 29}}} Expand
{{{B^2 + 7B + 7B + 49 + B^2 = 29}}} Combine like terms
{{{2B^2 + 14B + 49 = 29}}}  Subtract 29 from both sides
{{{2B^2 + 14B + 20 = 0}}} Factor out a 2 on the left side
{{{2*(B^2 + 7B + 10) = 0}}} Divides both sides by 2
{{{B^2 + 7B + 10 = 0}}}
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Find the factor of 10: 1,2,5,10
2 & 5 fit the equation
{{{B^2 + 7B + 10 = 0}}} rewrite teh equation
{{{B + 5) * (B + 2) = 0}}}  There are two answers to solve for.
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{{{B + 5 = 0}}}
{{{highlight(B = -5)}}}
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{{{B + 2 = 0}}}
{{{highlight(B = -2)}}}
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Note that sice you have 2 B values, you will need to find 2 A values
Plug the B values into equation 1 to find A
Equation 1: {{{A = B + 7}}}
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{{{A = -5 + 7}}}
{{{highlight(A = 2)}}}
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{{{A = -2 + 7}}}
{{{highlight(A = 5)}}}

So you have two solutions:
The numbers can be -5 and 2
or they can be -2 and 5