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

Solve for x: Solve the second equation for x. The second equation is -3x + 3 = y. To solve for x, we can rewrite it as -3x = y - 3 and then divide both sides by -3 to isolate x. -3x = y - 3 x = (y - 3) / -3 x = -(y - 3) / 3Substitute into first equation: Substitute the expression for x into the first equation. The first equation is 6x + 9y = 48. We will replace x with the expression we found in Step 1. 6(-(y - 3) / 3) + 9y = 48Simplify the equation: Simplify the equation. Distribute the 6 into the parentheses and simplify the equation. -2(y - 3) + 9y = 48 -2y + 6 + 9y = 48 7y + 6 = 48Solve for y: Solve for y. Subtract 6 from both sides of the equation to isolate the y term. 7y + 6 - 6 = 48 - 6 7y = 42 Now, divide both sides by 7 to solve for y. 7y / 7 = 42 / 7 y = 6Substitute back into x: Substitute the value of y back into the expression for x. Now that we know y is 6, we can substitute it back into the expression for x we found in Step 1. x = -(y - 3) / 3 x = -(6 - 3) / 3 x = -3 / 3 x = -1Write as ordered pair: Write the solution as an ordered pair (x, y). The solution to the system of equations is (-1, 6).

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Solve the system by substitution.

{:[6x+9y=48],[-3x+3=y]:}

(◻,◻)

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

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system by substitution.

\newline

\begin{aligned} 6 x+9 y & =48 \\ -3 x+3 & =y \end{aligned}

\newline

(\square, \square)

Solve for x: Solve the second equation for x. $\newline$ The second equation is $-3x + 3 = y$ . To solve for x, we can rewrite it as $-3x = y - 3$ and then divide both sides by $-3$ to isolate x. $\newline$ $-3x = y - 3$ $\newline$ $x = \frac{y - 3}{-3}$ $\newline$ $x = -\frac{y - 3}{3}$
Substitute into first equation: Substitute the expression for $x$ into the first equation. $\newline$ The first equation is $6x + 9y = 48$ . We will replace $x$ with the expression we found in Step $1$ . $\newline$ $6\left(-\frac{y - 3}{3}\right) + 9y = 48$
Simplify the equation: Simplify the equation. $\newline$ Distribute the $6$ into the parentheses and simplify the equation. $\newline$ $-2(y - 3) + 9y = 48$ $\newline$ $-2y + 6 + 9y = 48$ $\newline$ $7y + 6 = 48$
Solve for y: Solve for y. $\newline$ Subtract $6$ from both sides of the equation to isolate the $y$ term. $\newline$ $7y + 6 - 6 = 48 - 6$ $\newline$ $7y = 42$ $\newline$ Now, divide both sides by $7$ to solve for $y$ . $\newline$ $7y / 7 = 42 / 7$ $\newline$ $y = 6$
Substitute back into $x$ : Substitute the value of $y$ back into the expression for $x$ . Now that we know $y$ is $6$ , we can substitute it back into the expression for $x$ we found in Step $1$ . $x = -\frac{(y - 3)}{3}$ $x = -\frac{(6 - 3)}{3}$ $x = -\frac{3}{3}$ $x = -1$
Write as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution to the system of equations is $(-1, 6)$ .