Solve for x and y: 2x + 3y = 23 and 3x + y = 7

To solve the system of equations given by 2x + 3y = 23 and 3x + y = 7, we can use substitution or elimination methods. Here, we’ll use the substitution method for clarity.

First, we can express y in terms of x from the second equation:

3x + y = 7
=> y = 7 - 3x

Next, we substitute this expression for y into the first equation:

2x + 3(7 - 3x) = 23
=> 2x + 21 - 9x = 23
=> -7x + 21 = 23
=> -7x = 23 - 21
=> -7x = 2
=> x = -rac{2}{7}

With x now found, we can substitute x = -rac{2}{7} back into the equation for y:

y = 7 - 3(-rac{2}{7})
=> y = 7 + rac{6}{7}
=> y = rac{49}{7} + rac{6}{7}
=> y = rac{55}{7}

Therefore, the solution to the system of equations is:

x = -rac{2}{7}
 y = rac{55}{7}

This means that x is approximately -0.29 and y is approximately 7.86.