Solve the system by substitution. {:[8x-3y=-16],[7x+1=y]:} (◻,◻)

Substitute Equations: Substitute the second equation into the first equation. The second equation is given as 7x + 1 = y. We can use this to substitute for y in the first equation, 8x - 3y = -16.Use Substitution: Substitute y with 7x + 1 in the first equation. 8x - 3(7x + 1) = -16Distribute and Combine: Distribute -3 across the terms in the parentheses. 8x - 21x - 3 = -16Isolate x Term: Combine like terms. -13x - 3 = -16Solve for x: Add 3 to both sides of the equation to isolate the term with x. -13x = -16 + 3 -13x = -13Substitute x for y: Divide both sides by -13 to solve for x. x = (-13) / (-13) x = 1Calculate y Value: Substitute x back into the second equation to solve for y. 7x + 1 = y 7(1) + 1 = yCalculate the value of y. 7 + 1 = y y = 8

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Solve the system by substitution.

{:[8x-3y=-16],[7x+1=y]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} 8 x-3 y & =-16 \\ 7 x+1 & =y \end{aligned}$ $\newline$ $(\square, \square)$

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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} 8 x-3 y & =-16 \\ 7 x+1 & =y \end{aligned}

\newline

(\square, \square)

Substitute Equations: Substitute the second equation into the first equation. $\newline$ The second equation is given as $7x + 1 = y$ . We can use this to substitute for $y$ in the first equation, $8x - 3y = -16$ .
Use Substitution: Substitute $y$ with $7x + 1$ in the first equation. $8x - 3(7x + 1) = -16$
Distribute and Combine: Distribute $-3$ across the terms in the parentheses. $8x - 21x - 3 = -16$
Isolate $x$ Term: Combine like terms. $-13x - 3 = -16$
Solve for x: Add $3$ to both sides of the equation to isolate the term with $x$ . $\newline$ $-13x = -16 + 3$ $\newline$ $-13x = -13$
Substitute $x$ for $y$ : Divide both sides by $-13$ to solve for $x$ .
$x = (-13) / (-13)$
$x = 1$
Calculate $y$ Value: Substitute $x$ back into the second equation to solve for $y$ . $\newline$ $7x + 1 = y$ $\newline$ $7(1) + 1 = y$
Calculate y Value: Substitute $x$ back into the second equation to solve for $y$ . $\newline$ $7x + 1 = y$ $\newline$ $7(1) + 1 = y$ Calculate the value of $y$ . $\newline$ $7 + 1 = y$ $\newline$ $y = 8$