In each of the following questions, two equations are given. You have to solve them and
I. `2x+3y=7`
II. `4x+5y=19`

Options

A. If `xgty`
B. If `xley`
C. If `xgey`
D. If `xgty`

Answer

To solve the given equations step by step, we will follow the method of substitution or elimination. Here, we will use the elimination method.

### Step 1: Write down the given equations
We have the following two equations:
1. \( 2x + 3y = 7 \) (Equation I)
2. \( 4x + 5y = 19 \) (Equation II)

### Step 2: Make the coefficients of \( x \) the same
To eliminate \( x \), we can multiply Equation I by 2. This gives us:
\[ 2(2x + 3y) = 2(7) \]
\[ 4x + 6y = 14 \quad \text{(Equation III)} \]

### Step 3: Subtract Equation II from Equation III
Now, we will subtract Equation II from Equation III:
\[ (4x + 6y) - (4x + 5y) = 14 - 19 \]
This simplifies to:
\[ 6y - 5y = -5 \]
\[ y = -5 \]

### Step 4: Substitute the value of \( y \) back into Equation I
Now that we have found \( y \), we can substitute it back into Equation I to find \( x \):
\[ 2x + 3(-5) = 7 \]
This simplifies to:
\[ 2x - 15 = 7 \]
Adding 15 to both sides:
\[ 2x = 7 + 15 \]
\[ 2x = 22 \]
Dividing both sides by 2:
\[ x = 11 \]

### Step 5: Final values
Thus, the solution to the equations is:
\[ x = 11, \quad y = -5 \]

### Summary
The values of \( x \) and \( y \) are \( 11 \) and \( -5 \) respectively.

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