Solve by substitution:
4x-12y =5
-x + 3y = -1
4x-12y=5
4x+-12y+12y=5
4x/4=5/4
x=5/4 =1 1/4
4x+-12y=5
-4x+-12y=5
-12y/-12=5/-12
y=-5/12
-x+3y=-1
-x+3y-3y=-1
-x/-1=-1/-1
x=1
-x+3y=-1
-x+x+3y--1
3y/3=-1/3
y= -1/3
Carol! Thank you so much! I am to solve by substitution. I am a bit confused as to now having two separate y and x components, rather than one set of x and y/ If you have time, Please help me to understand/ Thank you. Carl
To solve this system of equations by substitution, we need to isolate one variable in one equation and substitute it into the other equation. Let's solve the equations step by step:
Step 1: Solve one equation for a variable.
Let's solve the second equation for x:
-x + 3y = -1
Add x to both sides:
3y = x - 1
Rearrange the equation:
x = 3y + 1
Step 2: Substitute the expression from step 1 into the other equation.
Now, substitute x = 3y + 1 into the first equation:
4x - 12y = 5
Replace x with 3y + 1:
4(3y + 1) - 12y = 5
Distribute 4 into (3y + 1):
12y + 4 - 12y = 5
Combine like terms:
4 = 5
Step 3: Analyzing the result.
If we look at the result, 4 = 5, it implies that the variables do not satisfy the original system of equations. In this case, the system is inconsistent and does not have a solution.
Therefore, the system of equations has no solution when solved by substitution.