Final answer:
To subtract the equations, eliminate one variable by multiplying the second equation by -1 and adding it to the first equation. Solve for the remaining variable. The solution to the system of equations is x = 3.5 and y = -5.5.
Step-by-step explanation:
To subtract the equations, you need to eliminate one variable so that you can solve for the remaining variable. In this case, you can eliminate the variable y by multiplying the second equation by -1 and adding it to the first equation.
Multiply the second equation by -1: (-1)(3x + 2y) = (-1)(3)
-3x - 2y = -3
Add this new equation to the first equation:
7x + 2y + (-3x - 2y) = 17 + (-3)
Combine like terms: 7x - 3x + 2y - 2y = 17 - 3
Simplify: 4x = 14
Divide both sides by 4 to solve for x: (4x)/4 = 14/4
x = 3.5
Now substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
7(3.5) + 2y = 17
28 + 2y = 17
Subtract 28 from both sides: 2y = 17 - 28
Simplify: 2y = -11
Divide both sides by 2 to solve for y: (2y)/2 = (-11)/2
y = -5.5
Therefore, the solution to the system of equations is x = 3.5 and y = -5.5.