Solve the system by substitution. {:[3y=x],[3x-4y=-25]:}

Identify Equation for Substitution: Identify the first equation to use for substitution. The first equation is 3y = x. We can use this to substitute for x in the second equation.Substitute in Second Equation: Substitute 3y for x in the second equation. The second equation is 3x - 4y = -25. Substituting 3y for x gives us 3(3y) - 4y = -25.Simplify and Solve for y: Simplify the equation and solve for y. 3(3y) - 4y = -25 simplifies to 9y - 4y = -25, which further simplifies to 5y = -25.Divide to Find y Value: Divide both sides by 5 to find the value of y. 5y = -25 divided by 5 gives y = -5.Substitute y back for x: Substitute y = -5 back into the first equation to find x. The first equation is 3y = x. Substituting -5 for y gives us 3(-5) = x.Calculate x Value: Calculate the value of x. 3(-5) = x simplifies to -15 = x. So, x = -15.

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Solve the system by substitution.

{:[3y=x],[3x-4y=-25]:}

Solve the system by substitution. $\newline$ $\begin{aligned} 3 y & =x \\ 3 x-4 y & =-25 \end{aligned}$

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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} 3 y & =x \\ 3 x-4 y & =-25 \end{aligned}

Identify Equation for Substitution: Identify the first equation to use for substitution. $\newline$ The first equation is $3y = x$ . We can use this to substitute for $x$ in the second equation.
Substitute in Second Equation: Substitute $3y$ for $x$ in the second equation. $\newline$ The second equation is $3x - 4y = -25$ . Substituting $3y$ for $x$ gives us $3(3y) - 4y = -25$ .
Simplify and Solve for y: Simplify the equation and solve for y. $3(3y) - 4y = -25$ simplifies to $9y - 4y = -25$ , which further simplifies to $5y = -25$ .
Divide to Find y Value: Divide both sides by $5$ to find the value of $y$ . $5y = -25$ divided by $5$ gives $y = -5$ .
Substitute $y$ back for $x$ : Substitute $y = -5$ back into the first equation to find $x$ . The first equation is $3y = x$ . Substituting $-5$ for $y$ gives us $3(-5) = x$ .
Calculate x Value: Calculate the value of x. $\newline$ $3(-5) = x$ simplifies to $-15 = x$ . So, $x = -15$ .