Question

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If 3x-4y=4 & x+2y=18, then evaculate x^2 +y^2 +xy=

Answer 1

129

Explanation:

`\left\{\begin{array}{ccc}3x-4y=4\\x+2y=18&\text{multiply both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x-4y=4\\2x+4y=36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=40\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=8}\\\\\text{Put the value of x to the second equation:}\\\\8+2y=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}`

`\text{Put the values of x and y to the expression}\ x^2+y^2+xy:\\\\8^2+5^2+(8)(5)=64+25+40=129`