Question

If x+y=10 and x-y=4 find the value of x2 y2

Answer 1

The answer is: 1323 .
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Step-by-step explanation:
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If x + y = 10 ; then: x = 10 - y ; and y = 10 - x ;

If x - y = 4 ; then x = 4 + y ;

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Start with: "x + y = 10" ;

Substitute "(4+y)" for "x" ;
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(4+y) + y = 10 ;
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4 + 2y = 10 ; subtract "4" from each side of the equation:
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4 + 2y - 4 = 10 - 4 ;
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2y = 6 ; divide each side of the equation by "2" ; to isolate "y" on one side of the equation; and to solve for "y";
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2y/2 = 6/2 ;
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to get: y = 3 ;
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Since: x + y = 10 ; substitute "3" for "y"; and solve for "x" :
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x + 3 = 10 ; subtract "3" from each side of the equation:
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x + 3 - 3 = 10 - 3 ;
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to get: x = 7 ;
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Now, the question asks: what is: x² * y² ?

x² * y² = 7² * 3³ = 49 * 27 = 1323 .
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Answer 2

You can solve this by substitution.
x+y=10
x-y=4
===== add the equations
2x=14
x=7

Then plug in x into one of the equations

7+y=10
y=3

so x^2=7*7=49
y^2=3*3=9

Hope that helps!