How to solve the system of equations 3 x + 2 y = 14 and y = x + 2 by substitution?

Question

How to solve the system of equations       3    x    +    2    y    =    14   and       y    =    x    +    2   by substitution?

Metafune7re · Accepted Answer

We can substitute (x + 2) for y in the first equation and solve for x since the second equation has already been solved for y:

3 x + 2 y = 14

becomes:

3 x + 2 (x + 2) = 14

3 x + (2 \times x) + (2 \times 2) = 14

3 x + 2 x + 4 = 14

(3 + 2) x + 4 = 14

5 x + 4 = 14

5 x + 4 - 4 = 14 - 4

5 x + 0 = 10

5 x = 10

\frac{5 x}{5} = \frac{10}{5}

\frac{5 x}{5} = 2

x = 2

Substitute 2 for x in the second solution and solve for y:

y = x + 2

becomes:

y = 2 + 2

y = 4

The Solution Is: x = 2 and y = 4 or (2, 4)

How to solve the system of equations 3 x + 2 y = 14 and...