Solve

2a + b = 3
4a - 5b = 20

My attempt
Multiply the first equation by 5
So,
10a + 5b = 15
4a - 5b = 20
Add them together
14a = 35
Divide both sides by 14
a = 2.5
Substitute (I have done it with the second one)
10 - 5b = 20
Take away 10 from both sides
5b = 10
Divide both sides by 5
b = 2

When I checked if the answers were right by fitting them back into the equation it didn't work

Please help

2a + b = 3 times TWO is easier

4 a + 2 b = 6
4 a - 5 b = 20
-------------------Subtract
0 a + 7 b = -14
so
b = -2 NOT PLUS 2
then
2 a -2 = 3
2 a = 5
a = 5/2
===========================
HERE is your error:
10 - 5b = 20
Take away 10 from both sides
- 5b = 10 NOTE MINUS SIGN!!!
Divide both sides by 5
b = -2

Thanks

Very much appreciated☆

its b =4

To solve the system of equations:

2a + b = 3 ...(1)
4a - 5b = 20 ...(2)

Your approach of multiplying the first equation by 5 to eliminate b is correct. However, let's go through the steps again.

Multiply equation (1) by 5:
5(2a + b) = 5(3)
10a + 5b = 15 ...(3)

Now, add equations (3) and (2) together:
(10a + 5b) + (4a - 5b) = 15 + 20
10a + 5b + 4a - 5b = 35

Combining like terms:
14a = 35

Next, divide both sides by 14:
a = 35/14
a = 2.5

Now that we have the value of a, substitute it back into equation (1) to find the value of b:
2(2.5) + b = 3
5 + b = 3
b = 3 - 5
b = -2

So, the solution to the system of equations is a = 2.5 and b = -2.

It seems that there might be a mistake when checking the solutions. Let's verify if they satisfy both equations:

For a = 2.5:
2(2.5) + (-2) = 3
5 - 2 = 3
3 = 3 (True)

4(2.5) - 5(-2) = 20
10 - (-10) = 20
10 + 10 = 20
20 = 20 (True)

Hence, the solutions a = 2.5 and b = -2 are indeed correct and satisfy both equations.

your error is in the 3rd last line

from :
10 - 5b = 20
-5b = 10
b = -2

btw, why didn't you sub back into
2a + b = 3, it would have been easier.
Also , it is not a good idea to sub into an equation that you have altered, try going back into the easiest-looking of the original.