Question

How to solve the equations

Answer 1

So first off, we need to establish that there are three terms that we need to find: a, c & E.

Let's write the three equations below:

Equation No. 1 -
a + c - 2E = 2

Equation No. 2 -
a - 2c = 5

Equation No. 3 -
- c + E = 4

To begin working out our answer, we will make (a) the subject of our second equation & (E) the subject of the third equation so that we can substitute them into the first equation as displayed below:

Equation No. 2 -
a - 2c = 5
a = 5 + 2c

Equation No. 3 -
- c + E = 4
E - c = 4
E = 4 + c

From there, we substitute the given equations for (a) & (E) into the first equation in order to make (c) the subject in the first equation as displayed below:

Equation No. 1 -
a + c - 2E = 2
( 5 + 2c ) + c - 2 ( 4 + c ) = 2
5 + 3c - 8 - 2c = 2
3c - 2c = 2 - 5 + 8
c = 5

Extending from this, by substituting the value of c, which is 5, into Equation No. 2 & 3, we will be able to also obtain the values of both (a) & (E) as displayed below:

Equation No. 2 -
a = 5 + 2c
a = 5 + 2 ( 5 )
a = 5 + 10
a = 15

Equation No. 3 -
E = 4 + c
E = 4 + ( 5 )
E = 9

Therefore, we have now successfully found the values of a, c & E as displayed below:

a = 15
c = 5
E = 9

If you want to check your answer, then simply substitue the values into Equation No. 1. If after solving the equations, the left-hand & right-hand side are equivalent, then the answer is correct. However, if it isn't equivalent, then the answer is either incorrect or you have made an error while solving thr equation. Here is the working out to check your answer for this question:

a + c - 2E = 2
( 15 ) + ( 5 ) - 2 ( 9 ) = 2
20 - 18 = 2
2 = 2

Therefore, the solution is correct.