To solve the system of linear equations using the substitution method, we can follow these steps:

Step 1: Choose one of the equations and solve for one of the variables in terms of the other variable. Let's choose the first equation:

-x + y = 2

Solving for y, we add x to both sides:

y = x + 2

Step 2: Substitute the expression for the solved variable from Step 1 into the other equation in the system and solve for the remaining variable. Let's substitute y = x + 2 into the second equation:

2x + 5(x + 2) = 9

Expanding the parentheses:

2x + 5x + 10 = 9

Combining like terms:

7x + 10 = 9

Subtracting 10 from both sides:

7x = -1

Dividing both sides by 7:

x = -1/7

Step 3: Substitute the value of the variable found in Step 2 back into the expression for the other variable from Step 1 to find its value. Let's substitute x = -1/7 into y = x + 2:

y = (-1/7) + 2

y = 13/7

So the solution to the system of linear equations is x = -1/7 and y = 13/7.