How do you solve this by substitution?
x=6y+2
3x-18y=4
This is the answer I get:
3(6y+2)-18y=4
18y+6-18y=4
18y+1818y+6-18y+18y=4
36y=10
36 36
Y=5/18
3x-18(5/18) =4
3x-5+5= 4+5
3x= 9
3 3
X=3
(3, 5/18)
To solve the system of equations by substitution, follow these steps:
1. Start with the first equation: x = 6y + 2.
2. Substitute the expression for x into the second equation: 3x - 18y = 4.
Now it becomes: 3(6y + 2) - 18y = 4.
3. Distribute the 3 to both terms inside the parentheses: 18y + 6 - 18y = 4.
4. Combine like terms: 18y + 6 - 18y = 4 simplifies to 6 = 4.
5. Since 6 does not equal 4, this means the system of equations is inconsistent and has no solution.
Therefore, there is no solution to this system of equations.
To solve the given system of equations using substitution, follow these steps:
1. Start with the first equation: x = 6y + 2.
2. Substitute this expression for x in the second equation: 3x - 18y = 4.
Replace x with (6y + 2): 3(6y + 2) - 18y = 4.
3. Simplify the equation by distributing and combining like terms:
18y + 6 - 18y = 4.
4. Cancel out like terms, which in this case are the 18y and -18y:
18y - 18y + 6 = 4.
5. Simplify further:
6 = 4.
6. At this point, the equation is not true, which means there is no solution to the system. The result suggests that the set of equations is inconsistent or contradictory.
Therefore, the given system of equations does not have a solution.
If you rearrange things a bit, you get
x - 6y = 2
3x - 18y = 4
which is the same as
x - 6y = 2
x - 6y = 4/3
The lines are parallel, so there is no intersection, and no solution to the equations.
Your answer fits the 2nd equation, but not the first.