Rewrite Equations: Step Title: Rewrite the System of Equations Concise Step Description: Rewrite the given system of equations for clarity. Calculation: The system of equations is: 1) y = -3x + 7 2) -2x - 3y = -7Substitute and Solve: Step Title: Substitute the First Equation into the Second Concise Step Description: Substitute the expression for y from the first equation into the second equation to solve for x. Calculation: Replace y in the second equation with -3x + 7: -2x - 3(-3x + 7) = -7Simplify Equation: Step Title: Simplify the Equation Concise Step Description: Distribute and combine like terms to simplify the equation. Calculation: -2x + 9x - 21 = -7 7x - 21 = -7Solve for x: Step Title: Solve for x Concise Step Description: Isolate x to find its value. Calculation: Add 21 to both sides of the equation: 7x - 21 + 21 = -7 + 21 7x = 14 Divide both sides by 7: x = 14 / 7 x = 2Substitute for y: Step Title: Substitute x Back into the First Equation Concise Step Description: Substitute the value of x back into the first equation to solve for y. Calculation: y = -3(2) + 7 y = -6 + 7 y = 1

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$y=-3x+7$ $\newline$ $-2x-3y=-7$

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y=-3x+7

\newline

-2x-3y=-7

Rewrite Equations: Step Title: Rewrite the System of Equations $\newline$ Concise Step Description: Rewrite the given system of equations for clarity. $\newline$ Calculation: The system of equations is: $\newline$ $1$ ) $y = -3x + 7$ $\newline$ $2$ ) $-2x - 3y = -7$
Substitute and Solve: Step Title: Substitute the First Equation into the Second $\newline$ Concise Step Description: Substitute the expression for $y$ from the first equation into the second equation to solve for $x$ . $\newline$ Calculation: Replace $y$ in the second equation with $-3x + 7$ : $\newline$ $-2x - 3(-3x + 7) = -7$
Simplify Equation: Step Title: Simplify the Equation $\newline$ Concise Step Description: Distribute and combine like terms to simplify the equation. $\newline$ Calculation: $-2x + 9x - 21 = -7$ $\newline$ $7x - 21 = -7$
Solve for x: Step Title: Solve for x $\newline$ Concise Step Description: Isolate x to find its value. $\newline$ Calculation: Add $21$ to both sides of the equation: $\newline$ $7x - 21 + 21 = -7 + 21$ $\newline$ $7x = 14$ $\newline$ Divide both sides by $7$ : $\newline$ $x = \frac{14}{7}$ $\newline$ $x = 2$
Substitute for y: Step Title: Substitute $x$ Back into the First Equation $\newline$ Concise Step Description: Substitute the value of $x$ back into the first equation to solve for $y$ . $\newline$ Calculation: $y = -3(2) + 7$ $\newline$ $y = -6 + 7$ $\newline$ $y = 1$