Solve the system by substitution. {:[-x+6y=30],[-y-2=x]:} (◻,◻)

Solve for x: Solve the second equation for x. The second equation is -y - 2 = x. We can rewrite this as x = -y - 2.Substitute x: Substitute x in the first equation with the expression found in Step 1. The first equation is -x + 6y = 30. Substituting x gives us -(-y - 2) + 6y = 30.Simplify the equation: Simplify the equation from Step 2. This simplifies to y + 2 + 6y = 30, which further simplifies to 7y + 2 = 30.Solve for y: Solve for y. Subtract 2 from both sides to get 7y = 28. Then divide both sides by 7 to find y = 4.Substitute y: Substitute y back into the equation x = -y - 2 to find x. Substitute y = 4 into x = -y - 2 to get x = -4 - 2, which simplifies to x = -6.Write the solution: Write the solution as an ordered pair (x, y). The solution is (-6, 4).

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Solve the system by substitution.

{:[-x+6y=30],[-y-2=x]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} -x+6 y & =30 \\ -y-2 & =x \end{aligned}$ $\newline$ $(\square, \square)$

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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} -x+6 y & =30 \\ -y-2 & =x \end{aligned}

\newline

(\square, \square)

Solve for $x$ : Solve the second equation for $x$ . The second equation is $-y - 2 = x$ . We can rewrite this as $x = -y - 2$ .
Substitute $x$ : Substitute $x$ in the first equation with the expression found in Step $1$ . $\newline$ The first equation is $-x + 6y = 30$ . Substituting $x$ gives us $-(-y - 2) + 6y = 30$ .
Simplify the equation: Simplify the equation from Step $2$ . $\newline$ This simplifies to $y + 2 + 6y = 30$ , which further simplifies to $7y + 2 = 30$ .
Solve for y: Solve for y. $\newline$ Subtract $2$ from both sides to get $7y = 28$ . Then divide both sides by $7$ to find $y = 4$ .
Substitute $y$ : Substitute $y$ back into the equation $x = -y - 2$ to find $x$ . Substitute $y = 4$ into $x = -y - 2$ to get $x = -4 - 2$ , which simplifies to $x = -6$ .
Write the solution: Write the solution as an ordered pair $x, y$ . The solution is $\left(-6, 4\right)$ .