Solve the system by substitution. {:[y=5x+2],[-3x+4y=-26]:}

Substitute y: Substitute y from the first equation into the second equation. Given the first equation y = 5x + 2, we can substitute y in the second equation -3x + 4y = -26.Replace y: Replace y in the second equation with 5x + 2. -3x + 4(5x + 2) = -26Distribute 4: Distribute 4 across the terms inside the parentheses. -3x + 20x + 8 = -26Combine like terms: Combine like terms. 17x + 8 = -26Subtract 8: Subtract 8 from both sides to isolate the term with x. 17x = -26 - 8Calculate right side: Calculate the right side of the equation. 17x = -34Divide both sides: Divide both sides by 17 to solve for x. x = -34 / 17Simplify fraction: Simplify the fraction to find the value of x. x = -2Substitute x back: Substitute x back into the first equation to solve for y. y = 5(-2) + 2Calculate value of y: Calculate the value of y. y = -10 + 2Simplify to find y: Simplify to find the value of y. y = -8Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (-2, -8).

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Solve the system by substitution.

{:[y=5x+2],[-3x+4y=-26]:}

Solve the system by substitution. $\newline$ $\begin{aligned} y & =5 x+2 \\ -3 x+4 y & =-26 \end{aligned}$

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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+2 \\ -3 x+4 y & =-26 \end{aligned}

Substitute $y$ : Substitute $y$ from the first equation into the second equation. $\newline$ Given the first equation $y = 5x + 2$ , we can substitute $y$ in the second equation $-3x + 4y = -26$ .
Replace $y$ : Replace $y$ in the second equation with $5x + 2$ . $\newline$ $-3x + 4(5x + 2) = -26$
Distribute $4$ : Distribute $4$ across the terms inside the parentheses. $\newline$ $-3x + 20x + 8 = -26$
Combine like terms: Combine like terms. $17x + 8 = -26$
Subtract $8$ : Subtract $8$ from both sides to isolate the term with $x$ . $\newline$ $17x = -26 - 8$
Calculate right side: Calculate the right side of the equation. $17x = -34$
Divide both sides: Divide both sides by $17$ to solve for $x$ . $\newline$ $x = -\frac{34}{17}$
Simplify fraction: Simplify the fraction to find the value of $x$ . $x = -2$
Substitute $x$ back: Substitute $x$ back into the first equation to solve for $y$ . $y = 5(-2) + 2$
Calculate value of y: Calculate the value of $y$ . $y = -10 + 2$
Simplify to find $y$ : Simplify to find the value of $y$ . $y = -8$
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-2, -8)$ .