{:[y=-x-3],[y=(1)/(3)x+5]:}

Set Equations Equal: We have a system of two equations: 1) y = -x - 3 2) y = (1/3)x + 5 To find the solution to the system, we need to find the values of x and y that satisfy both equations simultaneously.Solve for x: Since both equations equal y, we can set them equal to each other to find the value of x. So, -x - 3 = (1/3)x + 5Isolate x Term: To solve for x, we need to get all the x terms on one side and the constant terms on the other side. First, we'll add x to both sides to get: -x + x - 3 = (1/3)x + x + 5 This simplifies to: -3 = (4/3)x + 5Multiply by Reciprocal: Next, we'll subtract 5 from both sides to isolate the x term: -3 - 5 = (4/3)x + 5 - 5 This simplifies to: -8 = (4/3)xSubstitute x Value: Now, we'll multiply both sides by the reciprocal of (4/3) to solve for x: (3/4)(-8) = (3/4)(4/3)x This simplifies to: -6 = xFind y Value: Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. We'll use the first equation: y = -(-6) - 3Solving for y gives us: y = 6 - 3 y = 3

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$\begin{array}{l}y=-x-3 \\ y=\frac{1}{3} x+5\end{array}$

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\begin{array}{l}y=-x-3 \\ y=\frac{1}{3} x+5\end{array}

Set Equations Equal: We have a system of two equations: $\newline$ $1$ ) $y = -x - 3$ $\newline$ $2$ ) $y = \frac{1}{3}x + 5$ $\newline$ To find the solution to the system, we need to find the values of $x$ and $y$ that satisfy both equations simultaneously.
Solve for $x$ : Since both equations equal $y$ , we can set them equal to each other to find the value of $x$ . So, $-x - 3 = (\frac{1}{3})x + 5$
Isolate x Term: To solve for $x$ , we need to get all the $x$ terms on one side and the constant terms on the other side. $\newline$ First, we'll add $x$ to both sides to get: $\newline$ $-x + x - 3 = (\frac{1}{3})x + x + 5$ $\newline$ This simplifies to: $\newline$ $-3 = (\frac{4}{3})x + 5$
Multiply by Reciprocal: Next, we'll subtract $5$ from both sides to isolate the $x$ term: $\newline$ $-3 - 5 = (\frac{4}{3})x + 5 - 5$ $\newline$ This simplifies to: $\newline$ $-8 = (\frac{4}{3})x$
Substitute x Value: Now, we'll multiply both sides by the reciprocal of $(\frac{4}{3})$ to solve for x: $\newline$ $(\frac{3}{4})(-8) = (\frac{3}{4})(\frac{4}{3})x$ $\newline$ This simplifies to: $\newline$ $-6 = x$
Find y Value: Now that we have the value of $x$ , we can substitute it back into either of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $y = -(-6) - 3$
Find y Value: Now that we have the value of $x$ , we can substitute it back into either of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $y = -(-6) - 3$ Solving for $y$ gives us: $\newline$ $y = 6 - 3$ $\newline$ $y = 3$