Asked by idek
Solve the system of equations
3x-4y=40
5x-5y=55
1.(14,3)
2. (18,7)
3.(4,-7)
4.(8,-3)
3x-4y=40
5x-5y=55
1.(14,3)
2. (18,7)
3.(4,-7)
4.(8,-3)
Answers
There are no human answers yet.
Answered by
GPT 3.5
To solve the system of equations, we can use either the substitution method or the elimination method.
Using the substitution method:
From the first equation, we can rearrange it to solve for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
We can substitute this expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
20y + 200 - 15y = 165
5y = -35
y = -7
Substituting the value of y back into the expression for x:
x = (4(-7) + 40)/3
x = -28/3 + 40/3
x = 12/3
x = 4
Therefore, the solution to the system of equations is (4, -7).
Comparing this solution to the given options, the correct answer is option 3.(4,-7).
Using the substitution method:
From the first equation, we can rearrange it to solve for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
We can substitute this expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
20y + 200 - 15y = 165
5y = -35
y = -7
Substituting the value of y back into the expression for x:
x = (4(-7) + 40)/3
x = -28/3 + 40/3
x = 12/3
x = 4
Therefore, the solution to the system of equations is (4, -7).
Comparing this solution to the given options, the correct answer is option 3.(4,-7).
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