Questions: Solve the system of equations by graphing. 2x - y = 10 x + 2y = 5 Use the graphing tool to graph the two equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Solve the system of equations by graphing. 2x - y = 10 x + 2y = 5 Use the graphing tool to graph the two equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.
Transcript text: Solve the system of equations by graphing. \[ \begin{array}{l} 2 x-y=10 \\ x+2 y=5 \end{array} \] Use the graphing tool to graph the two equations. $\square$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $\square$ . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.
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Solution

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Solution Steps

Step 1: Rewrite the equations in slope-intercept form

The given system of equations is: \[ \begin{array}{l} 2x - y = 10 \\ x + 2y = 5 \end{array} \]

First, solve for \( y \) in terms of \( x \) for each equation.

For the first equation: \[ 2x - y = 10 \implies y = 2x - 10 \]

For the second equation: \[ x + 2y = 5 \implies 2y = -x + 5 \implies y = -\frac{1}{2}x + 2.5 \]

Step 2: Find the intersection point

Set the two equations equal to each other to find the intersection point: \[ 2x - 10 = -\frac{1}{2}x + 2.5 \]

Combine like terms: \[ 2x + \frac{1}{2}x = 10 + 2.5 \implies \frac{5}{2}x = 12.5 \implies x = 5 \]

Substitute \( x = 5 \) back into one of the original equations to find \( y \): \[ y = 2(5) - 10 = 0 \]

So, the solution is \( (5, 0) \).

Final Answer

The solution is \( (5, 0) \).

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