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

odveza6ad

odveza6ad

Answered question

2023-03-06

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

Answer & Explanation

Metafune7re

Metafune7re

Beginner2023-03-07Added 2 answers

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 × x ) + ( 2 × 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
5 x 5 = 10 5
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)

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