Solve the system by substitution. {:[y=2x-5],[y=7x]:} (◻,◻)

Set Equations Equal: Since both equations are already solved for y, we can set them equal to each other to find x. y = 2x - 5 y = 7x Set the right-hand sides equal to each other: 2x - 5 = 7xSolve for x: Solve for x by subtracting 2x from both sides of the equation. 2x - 5 - 2x = 7x - 2x -5 = 5xIsolate x: Divide both sides by 5 to isolate x. -5 / 5 = 5x / 5 x = -1Substitute x for y: Substitute x back into one of the original equations to find y. We can use y = 2x - 5. y = 2(-1) - 5 y = -2 - 5 y = -7Write Ordered Pair: Write the solution as an ordered pair (x, y). The solution is (-1, -7).

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Solve the system by substitution.

{:[y=2x-5],[y=7x]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{array}{l} y=2 x-5 \\ y=7 x \end{array}$ $\newline$ $(\square, \square)$

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Algebra 2

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system by substitution.

\newline

\begin{array}{l} y=2 x-5 \\ y=7 x \end{array}

\newline

(\square, \square)

Set Equations Equal: Since both equations are already solved for $y$ , we can set them equal to each other to find $x$ . $y = 2x - 5$ $y = 7x$ Set the right-hand sides equal to each other: $2x - 5 = 7x$
Solve for x: Solve for x by subtracting $2x$ from both sides of the equation. $\newline$ $2x - 5 - 2x = 7x - 2x$ $\newline$ $-5 = 5x$
Isolate x: Divide both sides by $5$ to isolate $x$ . $-\frac{5}{5} = \frac{5x}{5}$ $x = -1$
Substitute $x$ for $y$ : Substitute $x$ back into one of the original equations to find $y$ . We can use $y = 2x - 5$ . $y = 2(-1) - 5$ $y = -2 - 5$ $y = -7$
Write Ordered Pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-1, -7)$ .