Solve the system by substitution. {:[x=-3y+7],[-4x-5y=7]:}

Substitute x in second equation: Substitute the expression for x from the first equation into the second equation. Given the first equation x = -3y + 7, we can substitute this into the second equation -4x - 5y = 7.Perform substitution: Perform the substitution. Substitute x = -3y + 7 into -4x - 5y = 7. -4(-3y + 7) - 5y = 7Distribute and simplify: Distribute -4 across the terms in the parentheses. -4 * -3y + -4 * 7 - 5y = 7 12y - 28 - 5y = 7Combine like terms: Combine like terms. 12y - 5y - 28 = 7 7y - 28 = 7Isolate y term: Add 28 to both sides of the equation to isolate the term with y. 7y - 28 + 28 = 7 + 28 7y = 35Solve for y: Divide both sides by 7 to solve for y. 7y / 7 = 35 / 7 y = 5Substitute y in first equation: Substitute the value of y back into the first equation to solve for x. x = -3y + 7 x = -3(5) + 7Calculate x: Perform the calculation to find the value of x. x = -15 + 7 x = -8Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (-8, 5).

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Solve the system by substitution.

{:[x=-3y+7],[-4x-5y=7]:}

Solve the system by substitution. $\newline$ $\begin{aligned} x & =-3 y+7 \\ -4 x-5 y & =7 \end{aligned}$

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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 & =-3 y+7 \\ -4 x-5 y & =7 \end{aligned}

Substitute $x$ in second equation: Substitute the expression for $x$ from the first equation into the second equation. $\newline$ Given the first equation $x = -3y + 7$ , we can substitute this into the second equation $-4x - 5y = 7$ .
Perform substitution: Perform the substitution. $\newline$ Substitute $x = -3y + 7$ into $-4x - 5y = 7$ . $\newline$ $-4(-3y + 7) - 5y = 7$
Distribute and simplify: Distribute $-4$ across the terms in the parentheses. $\newline$ $-4 \times -3y + -4 \times 7 - 5y = 7$ $\newline$ $12y - 28 - 5y = 7$
Combine like terms: Combine like terms. $\newline$ $12y - 5y - 28 = 7$ $\newline$ $7y - 28 = 7$
Isolate y term: Add $28$ to both sides of the equation to isolate the term with $y$ . $\newline$ $7y - 28 + 28 = 7 + 28$ $\newline$ $7y = 35$
Solve for y: Divide both sides by $7$ to solve for y. $\newline$ $\frac{7y}{7} = \frac{35}{7}$ $\newline$ $y = 5$
Substitute $y$ in first equation: Substitute the value of $y$ back into the first equation to solve for $x$ . $x = -3y + 7$ $x = -3(5) + 7$
Calculate $x$ : Perform the calculation to find the value of $x$ . $x = -15 + 7$ $x = -8$
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-8, 5)$ .