Question

2a+3b=5
b=a-5 help please

Answer 1

a = -2

b = -7

Explanation:

the best method to solving this system of equations would be substitution since you are given an expression that equals one of the variables you're solving for (which is b = a - 5)

to begin, plug in a - 5 for b in the equation 2a + 3b = 5.

2a + 3b = 5 ⇒ 2a + 3(a - 5) = 5

the next step is to distribute 3 to a - 5. start with distributing 3 to a, which is just multiplying 3 · a. after that, you're left with a minus sign and 5, so that sign gets attached to the 5 and makes it a -5. distribute 3 to -5, which is just multiplying 3 · -5.

2a + 3(a - 5) = 5 ⇒ 2a + 3a - 15 = 5

since you have two terms with the variable a on one side of the equation (2a and 3a), combine the two like terms.

2a + 3a - 15 = 5 ⇒ 5a - 15 = 5

add 15 to both sides of the equation. on the left side, -15 and 15 cancel each other out because -15 + 15 = 0, leaving you with only 5a. on the right side of the equation, you have 5 - 15, which equals -10.

now your equation is 5a = -10.

divide both sides of the equation by 5. on the left side of the equation, you have 5a/5, which equals 1a, or a. on the right side, you have -10/5, which equals -2.

therefore a = -2.

now plug in -2 for a in b = a - 5 in order to solve for b!

b = a - 5 ⇒ b = -2 - 5

subtract -2 - 5.

b = -2 - 5 ⇒ b = -7

therefore b = -7.

your solutions are a = -2 and b = -7 :) i hope this helps! have a great day <3

Answer 2

2a + 3b = 5

b = a - 5

Explanation:

2a + 3b = 5

b = a - 5

You can write this another way:

2a + 3(a-5) = 5 ( I added the second formula in the first one )

Now you gotta factor out:

2a + 3a - 15 = 5

Here im gonna do plus 15

2a + 3a = 20 ==> 5a = 20

Now if you divide by 5, you get: a = 4

Now you can fill in the second formula again

b = a - 5 (ill fill this in now)

b = 4 - 5 = -1

So, this makes:

a = 4 , b = -1