Solve the system by substitution. {:[3y-8=x],[7x+10 y=37]:} (◻,◻)

Identify Equation for Substitution: Identify the first equation to use for substitution. The first equation is 3y - 8 = x. We can use this equation to express x in terms of y, which will allow us to substitute this expression into the second equation.Substitute Expression into Second Equation: Substitute the expression for x from the first equation into the second equation. The second equation is 7x + 10y = 37. Substituting x with 3y - 8 gives us: 7(3y - 8) + 10y = 37Distribute and Combine Like Terms: Distribute and combine like terms. 21y - 56 + 10y = 37 31y - 56 = 37Solve for y: Solve for y. Add 56 to both sides of the equation: 31y - 56 + 56 = 37 + 56 31y = 93 Now, divide both sides by 31: y = 93 / 31 y = 3Substitute Value Back for x: Substitute the value of y back into the first equation to solve for x. Using the first equation 3y - 8 = x, substitute y with 3: x = 3(3) - 8 x = 9 - 8 x = 1Write 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.

{:[3y-8=x],[7x+10 y=37]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} 3 y-8 & =x \\ 7 x+10 y & =37 \end{aligned}$ $\newline$ $(\square, \square)$

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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} 3 y-8 & =x \\ 7 x+10 y & =37 \end{aligned}

\newline

(\square, \square)

Identify Equation for Substitution: Identify the first equation to use for substitution. $\newline$ The first equation is $3y - 8 = x$ . We can use this equation to express $x$ in terms of $y$ , which will allow us to substitute this expression into the second equation.
Substitute Expression into Second Equation: Substitute the expression for $x$ from the first equation into the second equation. $\newline$ The second equation is $7x + 10y = 37$ . Substituting $x$ with $3y - 8$ gives us: $\newline$ $7(3y - 8) + 10y = 37$
Distribute and Combine Like Terms: Distribute and combine like terms. $\newline$ $21y - 56 + 10y = 37$ $\newline$ $31y - 56 = 37$
Solve for y: Solve for y. $\newline$ Add $56$ to both sides of the equation: $\newline$ $31y - 56 + 56 = 37 + 56$ $\newline$ $31y = 93$ $\newline$ Now, divide both sides by $31$ : $\newline$ $y = \frac{93}{31}$ $\newline$ $y = 3$
Substitute Value Back for x: Substitute the value of $y$ back into the first equation to solve for $x$ . Using the first equation $3y - 8 = x$ , substitute $y$ with $3$ : $x = 3(3) - 8$ $x = 9 - 8$ $x = 1$
Write Solution as Ordered Pair: Write the solution as an ordered pair $(x, y)$ . The solution is $(1, 3)$ .