Solve the system by substitution. {:[y=-7x-2],[-2x-2y=40]:}

Identify Equations: First, we need to identify the two equations in the system that we will be working with. Equation 1: y = -7x - 2 Equation 2: -2x - 2y = 40 We will use substitution to solve the system, which means we will substitute the expression for y from Equation 1 into Equation 2.Substitute y into Equation 2: Substitute y = -7x - 2 from Equation 1 into Equation 2. Equation 2 becomes: -2x - 2(-7x - 2) = 40 Now we need to simplify and solve for x.Simplify and Solve for x: Simplify the equation by distributing the -2 into the parentheses. -2x + 14x + 4 = 40 Combine like terms. 12x + 4 = 40Isolate x Term: Subtract 4 from both sides of the equation to isolate the term with x. 12x + 4 - 4 = 40 - 4 12x = 36Solve for x: Divide both sides by 12 to solve for x. 12x / 12 = 36 / 12 x = 3Substitute x into Equation 1: Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y. y = -7(3) - 2 Calculate the value of y. y = -21 - 2 y = -23Calculate y: We have found the values of x and y that satisfy both equations in the system. x = 3 and y = -23 These values are the solution to the system of equations.

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Solve the system by substitution.

{:[y=-7x-2],[-2x-2y=40]:}

Solve the system by substitution. $\newline$ $\begin{aligned} y & =-7 x-2 \\ -2 x-2 y & =40 \end{aligned}$

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Precalculus

Solve a system of equations in three variables using substitution

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Q. Solve the system by substitution.

\newline

\begin{aligned} y & =-7 x-2 \\ -2 x-2 y & =40 \end{aligned}

Identify Equations: First, we need to identify the two equations in the system that we will be working with. $\newline$ Equation $1$ : $y = -7x - 2$ $\newline$ Equation $2$ : $-2x - 2y = 40$ $\newline$ We will use substitution to solve the system, which means we will substitute the expression for $y$ from Equation $1$ into Equation $2$ .
Substitute $y$ into Equation $2$ : Substitute $y = -7x - 2$ from Equation $1$ into Equation $2$ . $\newline$ Equation $2$ becomes: $-2x - 2(-7x - 2) = 40$ $\newline$ Now we need to simplify and solve for $x$ .
Simplify and Solve for x: Simplify the equation by distributing the $-2$ into the parentheses. $\newline$ $-2x + 14x + 4 = 40$ $\newline$ Combine like terms. $\newline$ $12x + 4 = 40$
Isolate x Term: Subtract $4$ from both sides of the equation to isolate the term with $x$ . $\newline$ $12x + 4 - 4 = 40 - 4$ $\newline$ $12x = 36$
Solve for x: Divide both sides by $12$ to solve for x. $\newline$ $\frac{12x}{12} = \frac{36}{12}$ $\newline$ $x = 3$
Substitute $x$ into Equation $1$ : Now that we have the value of $x$ , we can substitute it back into Equation $1$ to find the value of $y$ . $\newline$ $y = -7(3) - 2$ $\newline$ Calculate the value of $y$ . $\newline$ $y = -21 - 2$ $\newline$ $y = -23$
Calculate $y$ : We have found the values of $x$ and $y$ that satisfy both equations in the system. $\newline$ $x = 3$ and $y = -23$ $\newline$ These values are the solution to the system of equations.