Solve the system by substitution. {:[-x-3y=-35],[2x=y]:} (◻,◻)

Identify easier equation: Identify the easier equation to substitute from. In this case, the second equation 2x = y is easier to use for substitution because it can be directly solved for y.Solve for y: Solve the second equation for y. We have 2x = y, so y = 2x.Substitute into first equation: Substitute y = 2x into the first equation -x - 3y = -35. This gives us -x - 3(2x) = -35.Simplify and solve for x: Simplify and solve for x. The equation becomes -x - 6x = -35, which simplifies to -7x = -35.Divide by -7: Divide both sides of the equation by -7 to find the value of x. This gives us x = (-35)/(-7), so x = 5.Substitute x back in: Substitute x = 5 back into the equation y = 2x to find the value of y. This gives us y = 2(5), so y = 10.Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (5, 10).

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Solve the system by substitution.

{:[-x-3y=-35],[2x=y]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} -x-3 y & =-35 \\ 2 x & =y \end{aligned}$ $\newline$ $(\square, \square)$

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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} -x-3 y & =-35 \\ 2 x & =y \end{aligned}

\newline

(\square, \square)

Identify easier equation: Identify the easier equation to substitute from. In this case, the second equation $2x = y$ is easier to use for substitution because it can be directly solved for $y$ .
Solve for y: Solve the second equation for y. We have $2x = y$ , so $y = 2x$ .
Substitute into first equation: Substitute $y = 2x$ into the first equation $-x - 3y = -35$ . This gives us $-x - 3(2x) = -35$ .
Simplify and solve for x: Simplify and solve for x. The equation becomes $-x - 6x = -35$ , which simplifies to $-7x = -35$ .
Divide by $-7$ : Divide both sides of the equation by $-7$ to find the value of $x$ . This gives us $x = (-35)/(-7)$ , so $x = 5$ .
Substitute $x$ back in: Substitute $x = 5$ back into the equation $y = 2x$ to find the value of $y$ . This gives us $y = 2(5)$ , so $y = 10$ .
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . The solution is $(5, 10)$ .