Questions: Solve the system of equations by graphing. 2x - y = 5 x + 2y = 5

Solve the system of equations by graphing. 2x - y = 5 x + 2y = 5
Transcript text: Solve the system of equations by graphing. \[ \begin{array}{l} 2 x-y=5 \\ x+2 y=5 \end{array} \]
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Solution

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Solution Steps

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

The first equation is \( 2x - y = 5 \). Solving for \( y \), we get:

\[ y = 2x - 5 \]

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

The second equation is \( x + 2y = 5 \). Solving for \( y \), we get:

\[ y = \frac{5 - x}{2} \]

Step 3: Find the intersection point

To find the intersection point, set the two expressions for \( y \) equal to each other:

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

Multiply through by 2 to clear the fraction:

\[ 4x - 10 = 5 - x \]

Add \( x \) to both sides:

\[ 5x - 10 = 5 \]

Add 10 to both sides:

\[ 5x = 15 \]

Divide by 5:

\[ x = 3 \]

Substitute \( x = 3 \) back into one of the original equations to find \( y \):

\[ y = 2(3) - 5 = 1 \]

The intersection point is \( (3, 1) \).

Final Answer

The solution to the system of equations is \( x = 3 \) and \( y = 1 \).

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = 2x - 5", "y = (5 - x)/2"], "latex_expressions": ["$y = 2x - 5$", "$y = \\frac{5 - x}{2}$"]}

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