To solve the two equations 3x - 2y = 10 and x + 3y = 7 simultaneously, we need to find the values of x and y that satisfy both equations. To do this, we'll use a method called substitution.
First, we'll solve one of the equations for one of the variables. Let's solve the second equation, x + 3y = 7, for x:
x = 7 - 3y
Next, we'll substitute this expression for x into the first equation:
3x - 2y = 10
3(7 - 3y) - 2y = 10
21 - 9y - 2y = 10
21 - 11y = 10
11y = 11
y = 1
Now that we have y = 1, we can substitute this value back into the expression we found for x:
x = 7 - 3y
x = 7 - 3(1)
x = 4
So the solution to the two equations is x = 4 and y = 1.