Y= 3x - 10
y= 2x - 5

The solution to the system of equations is x = 5 and y = 5. The coordinates (5, 5) represent the point where the two lines intersect in the xy-plane, and it is the unique solution to this system of linear equations.

Given that the system of equations:

y = 3x - 10                                     (1)

y = 2x - 5                                       (2)  

Since both equations are set equal to y, equate the right-hand sides of the equations since they represent the same value of y:

3x - 10 = 2x - 5

Now, let's solve for x:

3x - 2x = -5 + 10

x = 5

Now, found the value of x, substitute it back into either of the original equations to find the corresponding value of y.

Let's use the equation (1):

y = 3x - 10

y = 3(5) - 10

y = 15 - 10

y = 5

Hence, the values of x and y are 5 and 5. The system of equations have unique solution.

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Complete question:

Solve the system of equations for x and y:

If you're looking for a solution for both equations and had a choice between the 3 ways of solving it, I would choose substitution for this problem. So..

2x-5=3x-10

Move like terms to their own sides.

Take 2x away from both sides, and add 10 to both sides. That should leave you with

5=x

Now that you have the x, plug it into the equation that works best for you to solve.

That should be y=2(5)-5

y=10-5

y=5

(5,5) is your solution.