Solve the system by substitution. {:[y=-4x-7],[-7x+10 y=-23]:}

Substitute y into second equation: Substitute the expression for y from the first equation into the second equation. Given the system of equations: y = -4x - 7 -7x + 10y = -23 Substitute y = -4x - 7 into the second equation: -7x + 10(-4x - 7) = -23Distribute and simplify: Distribute 10 to the terms inside the parentheses and simplify. -7x - 40x - 70 = -23 Combine like terms: -47x - 70 = -23Add 70 to isolate x: Add 70 to both sides of the equation to isolate the term with x. -47x - 70 + 70 = -23 + 70 -47x = 47Divide to solve for x: Divide both sides by -47 to solve for x. -47x / -47 = 47 / -47 x = -1Substitute x into first equation: Substitute x = -1 into the first equation to solve for y. y = -4(-1) - 7 y = 4 - 7 y = -3Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (-1, -3).

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Solve the system by substitution.

{:[y=-4x-7],[-7x+10 y=-23]:}

Solve the system by substitution. $\newline$ $\begin{aligned} y & =-4 x-7 \\ -7 x+10 y & =-23 \end{aligned}$

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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} y & =-4 x-7 \\ -7 x+10 y & =-23 \end{aligned}

Substitute $y$ into second equation: Substitute the expression for $y$ from the first equation into the second equation. $\newline$ Given the system of equations: $\newline$ $y = -4x - 7$ $\newline$ $-7x + 10y = -23$ $\newline$ Substitute $y = -4x - 7$ into the second equation: $\newline$ $-7x + 10(-4x - 7) = -23$
Distribute and simplify: Distribute $10$ to the terms inside the parentheses and simplify. $\newline$ $-7x - 40x - 70 = -23$ $\newline$ Combine like terms: $\newline$ $-47x - 70 = -23$
Add $70$ to isolate x: Add $70$ to both sides of the equation to isolate the term with x. $\newline$ $-47x - 70 + 70 = -23 + 70$ $\newline$ $-47x = 47$
Divide to solve for x: Divide both sides by $-47$ to solve for $x$ . $-47x / -47 = 47 / -47$ $x = -1$
Substitute $x$ into first equation: Substitute $x = -1$ into the first equation to solve for $y$ . $\newline$ $y = -4(-1) - 7$ $\newline$ $y = 4 - 7$ $\newline$ $y = -3$
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-1, -3)$ .