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4a+5b+4c=29 and5a-4b-5c=36then a+c= Related: Linear Equations - Algeb...
Linear Equations - Algebra, Quantitative Reasoning
Given:
4a + 5b + 4c = 29
5a - 4b - 5c = 36
Step 1: Solve for a or c
First, we need to solve for either a or c. Let's solve for a:
4a + 5b + 4c = 29
4a = 29 - 5b - 4c
a = (29 - 5b - 4c)/4
Now we can substitute this value of a into the second equation:
5((29 - 5b - 4c)/4) - 4b - 5c = 36
Simplifying:
29 - 5b - 4c - 4b - 5c = 36(4/5)
-9b - 9c = -7
b + c = 7/9
Step 2: Solve for ac
Now we can solve for ac by substituting this value of b + c into the first equation:
4a + 5b + 4c = 29
4a + 5(7/9 - c) + 4c = 29
Simplifying:
4a + (35/9 - 5c) + 4c = 29
4a - c = 2/9
Multiplying both sides by c:
4ac - c^2 = 2c/9
4ac = 2c/9 + c^2
4ac = c(2/9 + c)
a*c = (2/9 + c)/4
Step 3: Substitute value of c
We can now substitute any value we have for c to find the corresponding value of ac. For example, if we know that c = 1, then:
a*c = (2/9 + 1)/4 = 11/36
Conclusion
Therefore, the value of ac depends on the value of c. We can find the corresponding value of ac by substituting any value we have for c into the expression a*c = (2/9 + c)/4.
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4a+5b+4c=29 and5a-4b-5c=36then a+c= Related: Linear Equations - Algebra, Quantitative Reasoning?
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