Questions: Solve the system of equations graphically. y=2x-8 y=3x+8

Solve the system of equations graphically. y=2x-8 y=3x+8
Transcript text: Solve the system of equations graphically. \[ \left\{\begin{array}{l} y=2 x-8 \\ y=3 x+8 \end{array}\right. \]
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Solution

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Solution Steps

Step 1: Identify the Equations

The given system of equations is: \[ y = 2x - 8 \] \[ y = 3x + 8 \]

Step 2: Graph the First Equation

Graph the equation \( y = 2x - 8 \). This is a linear equation with a slope of 2 and a y-intercept of -8.

Step 3: Graph the Second Equation

Graph the equation \( y = 3x + 8 \). This is a linear equation with a slope of 3 and a y-intercept of 8.

Step 4: Find the Intersection Point

The solution to the system of equations is the point where the two lines intersect.

Step 5: Verify the Intersection Point

To find the intersection point algebraically, set the equations equal to each other: \[ 2x - 8 = 3x + 8 \] Solve for \( x \): \[ 2x - 3x = 8 + 8 \] \[ -x = 16 \] \[ x = -16 \]

Substitute \( x = -16 \) back into one of the original equations to find \( y \): \[ y = 2(-16) - 8 \] \[ y = -32 - 8 \] \[ y = -40 \]

Final Answer

The intersection point is \((-16, -40)\). The correct graph is the one that shows the lines intersecting at this point.

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