What is the solution to the system of equations: \( 2x + 3y = 6 \) and \( 4x - y = 5 \)?

What is the solution to the system of equations: \( 2x + 3y = 6 \) and \( 4x - y = 5 \)?

• A. (1, 2)
• B. (0, 3)
• C. (2, 0)
• D. (3, 1)

Answer: (C)

To find the solution to the system of equations \(2x + 3y = 6\) and \(4x - y = 5\), we can solve it using the method of substitution or elimination. First, let's express \(y\) from the first equation. Rearranging \(2x + 3y = 6\) gives: \[3y = 6 - 2x\] Dividing everything by 3: \[y = 2 - \frac{2}{3}x\] Next, we substitute this expression for \(y\) into the second equation \(4x - y = 5\). Substituting gives: \[4x - \left(2 - \frac{2}{3}x\right) = 5\] This simplifies to: \[4x - 2 + \frac{2}{3}x = 5\] Combining like terms, we convert \(4x\) to a fraction: \(\frac{12}{3}x - 2 + \frac{2}{3}x = 5\) Adding the fractions results in: \[\left(\frac{12 + 2}{3}\

To find the solution to the system of equations (2x + 3y = 6) and (4x - y = 5), we can solve it using the method of substitution or elimination.

First, let's express (y) from the first equation. Rearranging (2x + 3y = 6) gives:

[3y = 6 - 2x]

Dividing everything by 3:

[y = 2 - \frac{2}{3}x]

Next, we substitute this expression for (y) into the second equation (4x - y = 5). Substituting gives:

[4x - \left(2 - \frac{2}{3}x\right) = 5]

This simplifies to:

[4x - 2 + \frac{2}{3}x = 5]

Combining like terms, we convert (4x) to a fraction:

(\frac{12}{3}x - 2 + \frac{2}{3}x = 5)

Adding the fractions results in:

[\left(\frac{12 + 2}{3}\