Hello, I need help solving two systems of equations. I'm not sure how to solve them. They are:
7w+e=8
e+5=9
And the second one is:
7e=107-6d
7e+8d=117
Thanks!
#1,
from the 2nd,
e = 4
sub that into the first:
7w + 4 = 8
7w = 4
w = 4/7
I feel suspicious that this problem contained a typo
#2
just use substitution,
since 7e = 107 - 6d
in the 2nd:
107 - 6d + 8d = 117
2d = 10
d = 5
then 7e = 107 - 6(5)
7e = 77
e = 11
Thank you so much! Oh, and I checked and the first problem doesn't contain a typo.
Hello! I can help you solve these systems of equations. Let's start with the first one:
1. 7w + e = 8
e + 5 = 9
To solve this system, we can use the method of substitution. In the second equation, we can solve for e and substitute that value into the first equation.
2. e + 5 = 9
Subtracting 5 from both sides,
e = 4
Now, substitute the value of e back into the first equation:
3. 7w + e = 8
7w + 4 = 8
Subtracting 4 from both sides,
7w = 4
To get w alone, divide both sides of the equation by 7:
4. w = 4/7
Therefore, the solution to this system of equations is w = 4/7 and e = 4.
Now, let's move on to the second system of equations:
1. 7e = 107 - 6d
7e + 8d = 117
Again, we will solve this system using the method of substitution. We can solve Equation 1 for e and substitute that value into Equation 2.
2. 7e = 107 - 6d
Dividing both sides by 7,
e = (107 - 6d)/7
Now, substitute the value of e back into the second equation:
3. 7e + 8d = 117
7((107 - 6d)/7) + 8d = 117
Simplifying,
107 - 6d + 8d = 117
Combining like terms,
2d = 10
Dividing both sides by 2,
d = 5
Now, substitute the value of d back into the equation we found for e:
4. e = (107 - 6d)/7
e = (107 - 6(5))/7
Simplifying,
e = (107 - 30)/7
e = 77/7
e = 11
Therefore, the solution to this second system of equations is e = 11 and d = 5.
I hope this helps! Let me know if you have any further questions.