how would you solve the following by substitution? {4y-5x=9

{x-4y=11

PLZ HELP!!! THNX!

from the second : x = 4y+11

sub that into the first
4y - 5(4y+11) = 9
4y - 20y - 55 = 9
-16y = 64
y = -4
then x = 4(-4) + 11 = -5

x = -5 , y = 4

To solve the system of equations using the substitution method, we'll solve one equation for one variable and substitute it into the other equation. Let's solve the second equation for x:

x - 4y = 11

We isolate x by adding 4y to both sides:

x = 11 + 4y

Now we substitute this expression for x into the first equation:

4y - 5x = 9

4y - 5(11 + 4y) = 9

Simplify the equation:

4y - 55 - 20y = 9

Combine like terms:

-16y - 55 = 9

To isolate y, we add 55 to both sides:

-16y = 9 + 55

-16y = 64

Divide by -16:

y = 64 / -16

y = -4

Now we substitute this value of y back into the second equation to find x:

x - 4(-4) = 11

x + 16 = 11

Subtract 16 from both sides:

x = 11 - 16

x = -5

The solution to the system of equations is x = -5 and y = -4.

To solve the given system of equations by substitution, we will use one equation to solve for one variable and then substitute that value into the other equation.

Let's solve the second equation for x:
x - 4y = 11

Rearranging the equation, we have:
x = 4y + 11

Now we can substitute this value of x into the first equation:

4y - 5x = 9

4y - 5(4y + 11) = 9

Now we can simplify and solve for y:

4y - 20y - 55 = 9

-16y - 55 = 9

-16y = 9 + 55

-16y = 64

Dividing both sides by -16, we get:

y = -4

Now substitute this value of y back into the second equation to find x:

x - 4(-4) = 11

x + 16 = 11

Subtracting 16 from both sides, we get:

x = 11 - 16

x = -5

So the solution to the given system of equations is x = -5 and y = -4.