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If $x^{2}-y^{2}=24$ , $x+y=8$ , then $3x-3y=$

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Find the roots of factored polynomials

Full solution

Q. If

x^{2}-y^{2}=24

,

x+y=8

, then

3x-3y=

Identify Relationship: Identify the relationship between $x$ and $y$ using the difference of squares formula: $x^2 - y^2 = (x + y)(x - y) = 24$ .
Substitute and Solve: Substitute $x + y = 8$ into the equation: $\newline$ $(x + y)(x - y) = 24$ $\newline$ $8(x - y) = 24$ $\newline$ $x - y = \frac{24}{8}$ $\newline$ $x - y = 3$ .
Calculate $3x - 3y$ : Solve for $x$ and $y$ using the system of equations: $\newline$ $x + y = 8$ $\newline$ $x - y = 3$ $\newline$ Adding these equations: $\newline$ $2x = 11$ $\newline$ $x = \frac{11}{2}$ $\newline$ $x = 5.5$ $\newline$ Substituting $x$ back into $x + y = 8$ : $\newline$ $x$ $0$ $\newline$ $x$ $1$ $\newline$ $x$ $2$ .
Calculate $3x - 3y$ : Solve for $x$ and $y$ using the system of equations: $\newline$ $x + y = 8$ $\newline$ $x - y = 3$ $\newline$ Adding these equations: $\newline$ $2x = 11$ $\newline$ $x = \frac{11}{2}$ $\newline$ $x = 5.5$ $\newline$ Substituting $x$ back into $x + y = 8$ : $\newline$ $5.5 + y = 8$ $\newline$ $y = 8 - 5.5$ $\newline$ $y = 2.5$ . Calculate $3x - 3y$ : $\newline$ $3x - 3y = 3(5.5) - 3(2.5)$ $\newline$ $= 16.5 - 7.5$ $\newline$ $x - y = 3$ $0$ .

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