Questions: Graph each equation. Estimate the solution of the system of equations. y-2x=0 y=4x-5

Graph each equation. Estimate the solution of the system of equations. y-2x=0 y=4x-5
Transcript text: Graph each equation. Estimate the solution of the system of equations. \[ \begin{array}{l} y-2 x=0 \\ y=4 x-5 \end{array} \]
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Solution

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Solution Steps

Step 1: Solve the first equation for \( y \)

The first equation is given by:

\[ y - 2x = 0 \]

To solve for \( y \), add \( 2x \) to both sides:

\[ y = 2x \]

Step 2: Solve the second equation for \( y \)

The second equation is already solved for \( y \):

\[ y = 4x - 5 \]

Step 3: Set the equations equal to find the intersection

Set the expressions for \( y \) from both equations equal to each other:

\[ 2x = 4x - 5 \]

Subtract \( 2x \) from both sides:

\[ 0 = 2x - 5 \]

Add 5 to both sides:

\[ 5 = 2x \]

Divide both sides by 2:

\[ x = \frac{5}{2} = 2.5 \]

Step 4: Substitute \( x = 2.5 \) back into one of the equations to find \( y \)

Substitute \( x = 2.5 \) into the first equation \( y = 2x \):

\[ y = 2(2.5) = 5 \]

Final Answer

The solution to the system of equations is \( x = 2.5 \) and \( y = 5 \).

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