Hi. I am having some problems with substitution method and i just can't seem to get these right. I have
1. 2x - 3y = -1 with y = x-1
2. -4x + y = 6 with -5x- y = 21 and finally,
3. -5x + y =-3 with 3x -8y = 24
2 x - 3(x-1) = -1
2 x - 3 x + 3 = -1
-x = -4
x = 4
y = x-1 = 3
etc
check
8 - 9 = -1 right
Hello! I'll be glad to help you with the substitution method for these equations.
Let's start with the first problem:
1. 2x - 3y = -1 with y = x - 1
To solve this system using the substitution method, we can substitute the value of y from the second equation into the first equation:
Substituting y = x - 1 into the first equation, we get:
2x - 3(x - 1) = -1
Simplifying the equation, we have:
2x - 3x + 3 = -1
-x + 3 = -1
Now, isolate x by subtracting 3 from both sides of the equation:
-x = -4
Finally, multiply both sides of the equation by -1 to solve for x:
x = 4
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use y = x - 1:
y = 4 - 1
y = 3
So the solution to the system of equations is x = 4 and y = 3.
Moving on to the second problem:
2. -4x + y = 6 with -5x - y = 21
Again, we'll solve this system using the substitution method by substituting y from the first equation into the second equation:
From the first equation, we have:
y = 4x + 6
Substituting this value of y into the second equation, we get:
-5x - (4x + 6) = 21
Distribute the negative sign and simplify:
-5x - 4x - 6 = 21
-9x - 6 = 21
Isolate x by adding 6 to both sides:
-9x = 27
Divide both sides of the equation by -9 to solve for x:
x = -3
Now, substitute the value of x back into either of the original equations to find the value of y. Let's use the first equation:
-4(-3) + y = 6
12 + y = 6
Subtract 12 from both sides of the equation:
y = 6 - 12
y = -6
Therefore, the solution to the system of equations is x = -3 and y = -6.
Finally, let's solve the third problem:
3. -5x + y = -3 with 3x - 8y = 24
Using the substitution method, we can solve this system by substituting y from the first equation into the second equation:
From the first equation, we have:
y = 5x - 3
Substituting this value of y into the second equation, we get:
3x - 8(5x - 3) = 24
Distribute the -8 and simplify:
3x - 40x + 24 = 24
-37x + 24 = 24
Subtract 24 from both sides of the equation to isolate the variable:
-37x = 0
Divide both sides of the equation by -37 to solve for x:
x = 0
Now, substitute the value of x back into either of the original equations to find the value of y. Let's use the first equation:
-5(0) + y = -3
y = -3
Hence, the solution to the system of equations is x = 0 and y = -3.
I hope this explanation helps you understand how to solve these problems using the substitution method! If you have any more questions, feel free to ask.