Solution to the simultaneous equation 3a+5b=7 and a-2b=4?

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the substitution method:

From the second equation, we can express a in terms of b:
a = 4 + 2b

Now substitute this expression for a into the first equation:
3(4 + 2b) + 5b = 7
12 + 6b + 5b = 7
11b = -5
b = -5/11

Now substitute the value of b back into the second equation to find the value of a:
a - 2(-5/11) = 4
a + 10/11 = 4
a = 4 - 10/11
a = 44/11 - 10/11
a = 34/11

Therefore, the solution to the simultaneous equations 3a + 5b = 7 and a - 2b = 4 is:
a = 34/11
b = -5/11

Step 1: Express one variable in terms of the other

From the second equation, we have:

```
a = 4 + 2b
```

Step 2: Substitute into the first equation

Substitute the expression for 'a' into the first equation:

```
3(4 + 2b) + 5b = 7
```

Step 3: Solve for 'b'

Simplify the equation:

```
12 + 6b + 5b = 7
11b = -5
b = -5/11
```

Step 4: Substitute 'b' back into the equation for 'a'

```
a = 4 + 2(-5/11)
a = 4 - 10/11
a = 36/11
```

Therefore, the solution to the simultaneous equations is:

```
a = 36/11
b = -5/11
```