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Solve the system by substitution. {:[6x+9y=48],[-3x+3=y]:} (◻,◻)

Solve the system by substitution.\newline6x+9y=48−3x+3=y \begin{aligned} 6 x+9 y & =48 \\ -3 x+3 & =y \end{aligned} \newline(□,□) (\square, \square)

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Q. Solve the system by substitution.\newline6x+9y=48−3x+3=y \begin{aligned} 6 x+9 y & =48 \\ -3 x+3 & =y \end{aligned} \newline(□,□) (\square, \square)
  1. Solve for x: Solve the second equation for x.\newlineThe second equation is −3x+3=y-3x + 3 = y. To solve for x, we can rewrite it as −3x=y−3-3x = y - 3 and then divide both sides by −3-3 to isolate x.\newline−3x=y−3-3x = y - 3\newlinex=y−3−3x = \frac{y - 3}{-3}\newlinex=−y−33x = -\frac{y - 3}{3}
  2. Substitute into first equation: Substitute the expression for xx into the first equation.\newlineThe first equation is 6x+9y=486x + 9y = 48. We will replace xx with the expression we found in Step 11.\newline6(−y−33)+9y=486\left(-\frac{y - 3}{3}\right) + 9y = 48
  3. Simplify the equation: Simplify the equation.\newlineDistribute the 66 into the parentheses and simplify the equation.\newline−2(y−3)+9y=48-2(y - 3) + 9y = 48\newline−2y+6+9y=48-2y + 6 + 9y = 48\newline7y+6=487y + 6 = 48
  4. Solve for y: Solve for y.\newlineSubtract 66 from both sides of the equation to isolate the yy term.\newline7y+6−6=48−67y + 6 - 6 = 48 - 6\newline7y=427y = 42\newlineNow, divide both sides by 77 to solve for yy.\newline7y/7=42/77y / 7 = 42 / 7\newliney=6y = 6
  5. Substitute back into xx: Substitute the value of yy back into the expression for xx. Now that we know yy is 66, we can substitute it back into the expression for xx we found in Step 11. x=−(y−3)3x = -\frac{(y - 3)}{3} x=−(6−3)3x = -\frac{(6 - 3)}{3} x=−33x = -\frac{3}{3} x=−1x = -1
  6. Write as ordered pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution to the system of equations is (−1,6)(-1, 6).

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