Solve the system of equations using linear combination.
a+c=9
8a+4.5c=58
8 a + 8.0 c = 72
8 a + 4.5 c = 58
----------------- subtract
3.5 c = 14
c = 4
so a = 5
To solve the system of equations using linear combination, we'll multiply the first equation by a suitable constant and add the resulting equations together to eliminate one of the variables.
1) Multiply the first equation by -8 to make the coefficients of "a" in both equations equal:
-8(a + c) = -8(9)
-8a - 8c = -72
2) Add the second equation to this newly obtained equation:
(-8a - 8c) + (8a + 4.5c) = -72 + 58
-8a + 8a - 8c + 4.5c = -14
Simplifying this equation, we get:
-3.5c = -14
3) Now, solve for "c" by dividing both sides of the equation by -3.5:
-3.5c / -3.5 = -14 / -3.5
c = 4
4) Substitute the value of "c" back into the first equation to solve for "a":
a + 4 = 9
a = 9 - 4
a = 5
Therefore, the solution to the system of equations is:
a = 5
c = 4