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Solve this system of equations by graphing. Graph the equations, then find the solution. $\newline$ $y = \frac{7}{4}x - 1$ $\newline$ $y = \frac{1}{2}x + 4$ $\newline$ Click to select points on the graph. $\newline$ $\newline$ The solution is $(\_, \_)$ .

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Find the magnitude of a three-dimensional vector

Full solution

Q. Solve this system of equations by graphing. Graph the equations, then find the solution.

\newline

y = \frac{7}{4}x - 1

\newline

y = \frac{1}{2}x + 4

\newline

Click to select points on the graph.

\newline

\newline

The solution is

(\_, \_)

.

Graph First Equation: Step $1$ : Graph the first equation $y = \frac{7}{4}x - 1$ . $\newline$ - Plot points by choosing values for $x$ and calculating $y$ . $\newline$ - For $x = 0$ , $y = -1$ $(0, -1)$ $\newline$ - For $x = 4$ , $y = 7$ $(4, 7)$ $\newline$ - Draw a line through these points.
Graph Second Equation: Step $2$ : Graph the second equation $y = \frac{1}{2}x + 4$ . $\newline$ - Plot points by choosing values for $x$ and calculating $y$ . $\newline$ - For $x = 0$ , $y = 4$ $(0, 4)$ $\newline$ - For $x = 4$ , $y = 6$ $(4, 6)$ $\newline$ - Draw a line through these points.
Find Intersection Point: Step $3$ : Find the intersection of the two lines. $\newline$ - From the graph, the lines intersect at $(8, 8)$ . $\newline$ - This point should satisfy both equations.
Check Solution: Step $4$ : Check the solution by substituting $x = 8$ into both equations. $\newline$ - For the first equation: $y = \frac{7}{4}\times8 - 1 = 14 - 1 = 13$ $\newline$ - For the second equation: $y = \frac{1}{2}\times8 + 4 = 4 + 4 = 8$ $\newline$ - There's a mismatch; the solution found does not satisfy both equations.

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