Solve the system by substitution. {:[y=-2x],[y=-6x+12]:} (◻,◻)

Identify Equations: Identify the two equations given in the system. The system of equations is: y = -2x y = -6x + 12Set Equations Equal: Since both equations are already solved for y, we can set them equal to each other to find the value of x. -2x = -6x + 12Add and Isolate Terms: Add 6x to both sides of the equation to isolate terms with x on one side. -2x + 6x = -6x + 6x + 12 4x = 12Solve for x: Divide both sides of the equation by 4 to solve for x. 4x / 4 = 12 / 4 x = 3Substitute and Solve for y: Substitute the value of x back into one of the original equations to solve for y. We can use y = -2x. y = -2(3) y = -6Write Ordered Pair: Write the solution as an ordered pair (x, y). The solution is (3, -6).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system by substitution.

{:[y=-2x],[y=-6x+12]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{array}{l} y=-2 x \\ y=-6 x+12 \end{array}$ $\newline$ $(\square, \square)$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system by substitution.

\newline

\begin{array}{l} y=-2 x \\ y=-6 x+12 \end{array}

\newline

(\square, \square)

Identify Equations: Identify the two equations given in the system. $\newline$ The system of equations is: $\newline$ $y = -2x$ $\newline$ $y = -6x + 12$
Set Equations Equal: Since both equations are already solved for $y$ , we can set them equal to each other to find the value of $x$ . $-2x = -6x + 12$
Add and Isolate Terms: Add $6x$ to both sides of the equation to isolate terms with $x$ on one side. $\newline$ $-2x + 6x = -6x + 6x + 12$ $\newline$ $4x = 12$
Solve for x: Divide both sides of the equation by $4$ to solve for x. $\newline$ $\frac{4x}{4} = \frac{12}{4}$ $\newline$ $x = 3$
Substitute and Solve for $y$ : Substitute the value of $x$ back into one of the original equations to solve for $y$ . We can use $y = -2x$ . $\newline$ $y = -2(3)$ $\newline$ $y = -6$
Write Ordered Pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(3, -6)$ .