I still don't know how to directly solve this problem. Can someone guide to solve this system of equation by using the substitution method? Thanks!

1. Y=6x-5
Y=-x+9

This was Damon's answer. Which part don't you understand?

"well, we know that both are y so
6x-5 = -x+9
7 x = 14
x = 2
then y = -x+9 = -2+9 = 7 ">""

How did you get 7 & 14?

6x-5 = -x+9

Add x to both sides of the equation

6x + x - 5 = -x + x + 9

7x - 5 = 9

Add 5 to both sides of the equation

7x = 14

Sure! To solve a system of equations using the substitution method, follow these steps:

Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for Y in terms of x:
Y = -x + 9

Step 2: Substitute the expression for Y from step 1 into the other equation. Let's substitute Y in the first equation:
6x - 5 = -x + 9

Step 3: Solve the resulting equation for x. Move all terms with x to one side and all constant terms to the other side:
6x + x = 9 + 5
7x = 14
x = 2

Step 4: Substitute the value of x back into one of the original equations to solve for the other variable. Let's substitute x = 2 into the second equation:
Y = -2 + 9
Y = 7

Step 5: Write the solution as an ordered pair (x, Y):
(2, 7)

Therefore, the solution to the system of equations is x = 2 and Y = 7.