I SERIOUSLY need help!

Solve the linear system by using substitution.
x=6-4y
2x-3y=1

Explanation too, please!
Please and thanks!

very very easy

sub x = 6-4y into
2x - 3y = 1
2(6-4y) - 3y = 1
12 - 8y - 3y = 1
-11y = -11
y = 1

then x = 6 - 4(1) = 2

Thank you, but:

How did you go from 12-8y-3y to -11y?

12 - 8y - 3y = 1

12 - 11y = 1 , that should be clear
12 -12 - 11y = 1 -12
-11y = -11
divide by -11
y = 1

Understood. Thank you.

To solve the linear system using substitution, we need to find the value of one variable in terms of the other and substitute it into the other equation. Let's start by solving the first equation for x.

Given:
1. x = 6 - 4y
2. 2x - 3y = 1

Step 1: Solve the first equation for x
From equation 1, we have x = 6 - 4y.

Step 2: Substitute x into the second equation
Now, substitute x in equation 2 with its value from equation 1.
2(6 - 4y) - 3y = 1

Step 3: Solve the equation for y
Now, simplify and solve the resulting equation from step 2:
12 - 8y - 3y = 1.
Combine like terms: -11y + 12 = 1.
Subtract 12 from both sides: -11y = -11.
Divide both sides by -11: y = 1.

Step 4: Substitute the value of y back into equation 1 to find x
Using the equation 1: x = 6 - 4y.
Substitute the value of y (which is 1) into equation 1:
x = 6 - 4(1),
x = 6 - 4,
x = 2.

Therefore, the solution to the linear system is x = 2, y = 1.

In summary, we solved the linear system by substituting the value of one variable (x) into the other equation. This technique allows us to eliminate one variable and find the value of the remaining variable.