Solve the system by substitution. {:[-7y-5=x],[-3x+2y=-8]:} (◻,◻)

Isolate x: Isolate x in the first equation -7y - 5 = x. Add 5 to both sides of the equation. -7y - 5 + 5 = x + 5 -7y = x + 5 Now, subtract 5 from both sides to get x by itself. -7y - 5 = xSubstitute x: Substitute -7y - 5 for x in the second equation -3x + 2y = -8. Replace x with -7y - 5 in the second equation. -3(-7y - 5) + 2y = -8Distribute and combine terms: Distribute -3 across the parentheses. -3 * -7y + (-3) * -5 + 2y = -8 21y + 15 + 2y = -8Isolate y-term: Combine like terms on the left side of the equation. 21y + 2y + 15 = -8 23y + 15 = -8Solve for y: Subtract 15 from both sides to isolate the y-term. 23y + 15 - 15 = -8 - 15 23y = -23Substitute y into first equation: Divide both sides by 23 to solve for y. 23y / 23 = -23 / 23 y = -1Find x: Substitute y = -1 back into the first equation -7y - 5 = x to solve for x. -7(-1) - 5 = x 7 - 5 = x x = 2Write solution: Write the solution as an ordered pair (x, y). The solution is (2, -1).

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Solve the system by substitution.

{:[-7y-5=x],[-3x+2y=-8]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{array}{c} -7 y-5=x \\ -3 x+2 y=-8 \end{array}$ $\newline$ $(\square, \square)$

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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{array}{c} -7 y-5=x \\ -3 x+2 y=-8 \end{array}

\newline

(\square, \square)

Isolate $x$ : Isolate $x$ in the first equation $-7y - 5 = x$ . Add $5$ to both sides of the equation. $-7y - 5 + 5 = x + 5$ $-7y = x + 5$ Now, subtract $5$ from both sides to get $x$ by itself. $-7y - 5 = x$
Substitute $x$ : Substitute $-7y - 5$ for $x$ in the second equation $-3x + 2y = -8$ . Replace $x$ with $-7y - 5$ in the second equation. $-3(-7y - 5) + 2y = -8$
Distribute and combine terms: Distribute $-3$ across the parentheses. $\newline$ $-3 \times -7y + (-3) \times -5 + 2y = -8$ $\newline$ $21y + 15 + 2y = -8$
Isolate y-term: Combine like terms on the left side of the equation. $\newline$ $21y + 2y + 15 = -8$ $\newline$ $23y + 15 = -8$
Solve for y: Subtract $15$ from both sides to isolate the y-term. $\newline$ $23y + 15 - 15 = -8 - 15$ $\newline$ $23y = -23$
Substitute $y$ into first equation: Divide both sides by $23$ to solve for $y$ . $\newline$ $\frac{23y}{23} = \frac{-23}{23}$ $\newline$ $y = -1$
Find $x$ : Substitute $y = -1$ back into the first equation $-7y - 5 = x$ to solve for $x$ .
$-7(-1) - 5 = x$
$7 - 5 = x$
$x = 2$
Write solution: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(2, -1)$ .