Solve the system by substitution. {:[y=5x-10],[-4x+3y=36]:}

Identify Equation: Identify the equation that can be easily substituted. In this case, we have y expressed in terms of x in the first equation: y = 5x - 10.Substitute Expression: Substitute the expression for y into the second equation. The second equation is -4x + 3y = 36. We will replace y with 5x - 10. -4x + 3(5x - 10) = 36Distribute and Combine: Distribute and combine like terms. -4x + 15x - 30 = 36 11x - 30 = 36Solve for x: Solve for x. Add 30 to both sides of the equation. 11x - 30 + 30 = 36 + 30 11x = 66 Divide both sides by 11. x = 66 / 11 x = 6Substitute for y: Substitute the value of x back into the first equation to solve for y. y = 5x - 10 y = 5(6) - 10 y = 30 - 10 y = 20Write Ordered Pair: Write the solution as an ordered pair (x, y). The solution is (6, 20).

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Solve the system by substitution.

{:[y=5x-10],[-4x+3y=36]:}

Solve the system by substitution. $\newline$ $\begin{aligned} y & =5 x-10 \\ -4 x+3 y & =36 \end{aligned}$

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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 & =5 x-10 \\ -4 x+3 y & =36 \end{aligned}

Identify Equation: Identify the equation that can be easily substituted. $\newline$ In this case, we have $y$ expressed in terms of $x$ in the first equation: $y = 5x - 10$ .
Substitute Expression: Substitute the expression for $y$ into the second equation. $\newline$ The second equation is $-4x + 3y = 36$ . We will replace $y$ with $5x - 10$ . $\newline$ $-4x + 3(5x - 10) = 36$
Distribute and Combine: Distribute and combine like terms. $\newline$ $-4x + 15x - 30 = 36$ $\newline$ $11x - 30 = 36$
Solve for x: Solve for x. $\newline$ Add $30$ to both sides of the equation. $\newline$ $11x - 30 + 30 = 36 + 30$ $\newline$ $11x = 66$ $\newline$ Divide both sides by $11$ . $\newline$ $x = \frac{66}{11}$ $\newline$ $x = 6$
Substitute for y: Substitute the value of $x$ back into the first equation to solve for $y$ . $\newline$ $y = 5x - 10$ $\newline$ $y = 5(6) - 10$ $\newline$ $y = 30 - 10$ $\newline$ $y = $20$
Write Ordered Pair: Write the solution as an ordered pair $(x, y)$. The solution is $(6, 20)$.