solve the system a+b=4 and a-2*b=1 — step-by-step solution

1) We have the following 2 equations:

[1]:

a + b = 4

[2]:

a - 2 b = 1

2) Let's solve for a:

a + b = 4

[1]

a + b = 4

Solution obtained [1]:

a = 4 - b

3) Solving for b:

a - 2 b = 1

[2] where

a = 4 - b

ⓘ Like terms are grouped by adding their coefficients:

- b - 2 b

-3 b

4 - 3 b = 1

ⓘ We gather the terms in

b

on the right and the other terms on the left

4 - 1 = 3 b

ⓘ Start from

4

and move back

1

on the number line:

4 - 1

3

3 = 3 b

ⓘ Divide both sides by

3

b = \frac{3}{3}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{3}{3}

1

Solution obtained [2]:

b = 1

4) We find the value of a using:

a = 4 - b

using

b = 1

a = 4 - 1

ⓘ Start from

4

and move back

1

on the number line:

4 - 1

3

Solution found:

a = 3

▶Solution:

{a = 3, b = 1}