{:[8x-y=12],[2x-6y=3]:} Consider the system of equations. If (x,y) is the solution to the system, then what is the value of x+y ?

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{:[8x-y=12],[2x-6y=3]:} Consider the system of equations. If  (x,y) is the solution to the system, then what is the value of  x+y ?

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Write Equations: Write down the system of equations. We have the following system of equations: {:[8x-y=12],[2x-6y=3]:}Multiply Second Equation: Multiply the second equation by 3 to make the coefficients of y the same. Multiplying the second equation by 3, we get: {:[8x-y=12],[6x-18y=9]:}Eliminate y: Subtract the second equation from the first equation to eliminate y. Subtracting the second equation from the first, we get: (8x - y) - (6x - 18y) = 12 - 9 This simplifies to: 8x - y - 6x + 18y = 3 Combining like terms, we get: 2x + 17y = 3Solve for y: Solve for y using the modified second equation. We can solve for y by rearranging the modified second equation: 2x + 17y = 3 17y = 3 - 2x y = (3 - 2x)/17Substitute for y: Substitute the expression for y back into the first original equation to solve for x. Substituting y = (3 - 2x)/17 into the first original equation 8x - y = 12, we get: 8x - (3 - 2x)/17 = 12 Multiplying through by 17 to clear the fraction, we get: 136x - (3 - 2x) = 204Correct Multiplication: Step 5 (Correction): Correct the multiplication to clear the fraction. Multiplying through by 17 to clear the fraction, we get: 17 * 8x - 17 * (3 - 2x)/17 = 17 * 12 This simplifies to: 136x - (3 - 2x) = 204 Now distribute the negative sign inside the parentheses: 136x - 3 + 2x = 204 Combine like terms: 138x - 3 = 204 Add 3 to both sides: 138x = 207 Divide both sides by 138: x = 207 / 138 Simplify the fraction: x = 1.5Substitute for x: Substitute the value of x back into the expression for y. Now that we have x = 1.5, we can substitute it back into the expression for y: y = (3 - 2x)/17 y = (3 - 2(1.5))/17 y = (3 - 3)/17 y = 0/17 y = 0Find x + y: Add the values of x and y to find x + y. x + y = 1.5 + 0 x + y = 1.5

$\begin{array}{l} 8 x-y=12 \\ 2 x-6 y=3 \end{array}$ $\newline$ Consider the system of equations. If $(x, y)$ is the solution to the system, then what is the value of $x+y$ ?

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$\begin{array}{l} 8 x-y=12 \\ 2 x-6 y=3 \end{array}$ $\newline$ Consider the system of equations. If $(x, y)$ is the solution to the system, then what is the value of $x+y$ ?