I need help solving each equation by the substitution method.

1. X=5y-1
X+2y=13

2. -2x+3y=11
X=4y-3

3. X=-9y-1
2x+4y=5

I need help on these so please guide me in the right direction because I'm struggling on this topic!!

1)

use 5 y - 1 for x
so
5 y-1 + 2y = 13
or
7 y - 1 = 13
7 y = 14
y = 2
now go back and get x
x = 5(2)-1
x = 9

2)

-2x+3y=11
X=4y-3

-2 (4y-3) + 3 y = 11

-8 y + 6 + 3 y = 11
- 5 y + 6 = 11
-5y = 5
y=-1
etc

Sure! I'd be happy to help. The substitution method involves substituting one variable in terms of the other from one equation into the other equation. Let's go through each problem step by step:

1. X = 5y - 1 and X + 2y = 13

First, we'll solve the first equation for X. We have X = 5y - 1.

Then, we'll substitute this value of X into the second equation. Instead of writing X, we'll write (5y - 1):

(5y - 1) + 2y = 13

Now, we solve this equation for y:

7y - 1 = 13
7y = 14
y = 2

Now that we have the value of y, we can substitute it back into the first equation to find X:

X = 5(2) - 1
X = 9

So, the solution to the system of equations is X = 9 and y = 2.

2. -2x + 3y = 11 and X = 4y - 3

First, let's solve the second equation for X. We have X = 4y - 3.

Now, we'll substitute this value of X into the first equation. Instead of writing X, we'll write (4y - 3):

-2(4y - 3) + 3y = 11

Now, we solve this equation for y:

-8y + 6 + 3y = 11
-5y + 6 = 11
-5y = 5
y = -1

Now that we have the value of y, we can substitute it back into the second equation to find X:

X = 4(-1) - 3
X = -4 - 3
X = -7

So, the solution to the system of equations is X = -7 and y = -1.

3. X = -9y - 1 and 2x + 4y = 5

First, we'll solve the first equation for X. We have X = -9y - 1.

Then, we'll substitute this value of X into the second equation. Instead of writing X, we'll write (-9y - 1):

2(-9y - 1) + 4y = 5

Now, we solve this equation for y:

-18y - 2 + 4y = 5
-14y - 2 = 5
-14y = 7
y = -0.5

Now that we have the value of y, we can substitute it back into the first equation to find X:

X = -9(-0.5) - 1
X = 4.5 - 1
X = 3.5

So, the solution to the system of equations is X = 3.5 and y = -0.5.

I hope this helps! Let me know if you have any more questions.