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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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