The graphs of y=2x-5 and x + 3y=-1 intersect at

Options

A. (-1,2)
B. (-2,-1)
C. (2,-1)
D. (-2,1)

Answer

To find the intersection point of the two lines given by the equations \( y = 2x - 5 \) and \( x + 3y = -1 \), we will follow these steps:

### Step 1: Write down the equations
The equations we have are:
1. \( y = 2x - 5 \) (Equation 1)
2. \( x + 3y = -1 \) (Equation 2)

### Step 2: Substitute Equation 1 into Equation 2
We will substitute the expression for \( y \) from Equation 1 into Equation 2:
\[ x + 3(2x - 5) = -1 \]

### Step 3: Simplify the equation
Now, we simplify the equation:
\[ x + 6x - 15 = -1 \]
Combine like terms:
\[ 7x - 15 = -1 \]

### Step 4: Solve for \( x \)
Add 15 to both sides:
\[ 7x = 14 \]
Now, divide by 7:
\[ x = 2 \]

### Step 5: Substitute \( x \) back to find \( y \)
Now that we have \( x = 2 \), we will substitute this value back into Equation 1 to find \( y \):
\[ y = 2(2) - 5 \]
Calculating this gives:
\[ y = 4 - 5 = -1 \]

### Step 6: Write the intersection point
The intersection point of the two lines is:
\[ (2, -1) \]

### Conclusion
Thus, the graphs of \( y = 2x - 5 \) and \( x + 3y = -1 \) intersect at the point \( (2, -1) \).

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