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y=x-6

y=-x+5

$2$ . $y=x-6$ $\newline$ $3$ . $y=-x+5$

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Composition of linear functions: find a value

Full solution

Q.

2

.

y=x-6

\newline

3

.

y=-x+5

Set Equations Equal: Set the two equations equal to each other to find the $x$ -coordinate of the intersection point. $\newline$ Since both equations equal $y$ , we can set them equal to each other: $\newline$ $x - 6 = -x + 5$
Solve for x: Solve for x by adding $x$ to both sides and adding $6$ to both sides to isolate $x$ . $\newline$ $x - 6 + x = -x + 5 + x$ $\newline$ $2x - 6 = 5$ $\newline$ $2x = 5 + 6$ $\newline$ $2x = 11$
Divide by $2$ : Divide both sides by $2$ to find the value of x. $\newline$ $\frac{2x}{2} = \frac{11}{2}$ $\newline$ $x = \frac{11}{2}$ $\newline$ $x = 5.5$
Substitute x Value: Substitute the value of $x$ back into one of the original equations to find the $y$ -coordinate of the intersection point. $\newline$ We can use the first equation $y = x - 6$ : $\newline$ $y = 5.5 - 6$ $\newline$ $y = -0.5$
Check Solution: Check the solution by substituting $x$ and $y$ into the second equation to ensure it is satisfied. $\newline$ Using the second equation $y = -x + 5$ : $\newline$ $-0.5 = -(5.5) + 5$ $\newline$ $-0.5 = -5.5 + 5$ $\newline$ $-0.5 = -0.5$ $\newline$ The solution satisfies both equations.

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