Solve the system by substitution. {:[3y=x],[2x-7y=9]:} (◻,◻)

Rewrite first equation for x: Solve the first equation for x. The first equation is 3y = x. To solve for x, we can simply rewrite it as x = 3y.Substitute x in second equation: Substitute x = 3y into the second equation. The second equation is 2x - 7y = 9. Substituting x with 3y gives us 2(3y) - 7y = 9.Simplify and solve for y: Simplify and solve for y. 2(3y) - 7y = 9 simplifies to 6y - 7y = 9, which further simplifies to -y = 9. To solve for y, we multiply both sides by -1, giving us y = -9.Substitute y in first equation: Substitute y = -9 back into the first equation to solve for x. The first equation is x = 3y. Substituting y with -9 gives us x = 3(-9).Calculate x value: Calculate the value of x. x = 3(-9) simplifies to x = -27.Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (-27, -9).

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Solve the system by substitution.

{:[3y=x],[2x-7y=9]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} 3 y & =x \\ 2 x-7 y & =9 \end{aligned}$ $\newline$ $(\square, \square)$

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Algebra 2

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system by substitution.

\newline

\begin{aligned} 3 y & =x \\ 2 x-7 y & =9 \end{aligned}

\newline

(\square, \square)

Rewrite first equation for $x$ : Solve the first equation for $x$ . The first equation is $3y = x$ . To solve for $x$ , we can simply rewrite it as $x = 3y$ .
Substitute $x$ in second equation: Substitute $x = 3y$ into the second equation. $\newline$ The second equation is $2x - 7y = 9$ . Substituting $x$ with $3y$ gives us $2(3y) - 7y = 9$ .
Simplify and solve for $y$ : Simplify and solve for $y$ . $2(3y) - 7y = 9$ simplifies to $6y - 7y = 9$ , which further simplifies to $-y = 9$ . To solve for $y$ , we multiply both sides by $-1$ , giving us $y = -9$ .
Substitute $y$ in first equation: Substitute $y = -9$ back into the first equation to solve for $x$ . The first equation is $x = 3y$ . Substituting $y$ with $-9$ gives us $x = 3(-9)$ .
Calculate x value: Calculate the value of x. $\newline$ $x = 3(-9)$ simplifies to $x = -27$ .
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-27, -9)$ .