Question

Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20​

Answer 1

`3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = (76)/(19) =4 \\ y = 14 - 3( 4 ) = 2 \\`

Answer 2

(4, 2 )

Explanation:

Given the 2 equations

3x + y = 14 → (1)

7x - 4y = 20 → (2)

Rearrange (1) making y the subject by subtracting 3x from both sides

y = 14 - 3x → (3)

Substitute y = 14 - 3x into (2)

7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side

7x - 56 + 12x = 20

19x - 56 = 20 ( add 56 to both sides )

19x = 76 ( divide both sides by 19 )

x = 4

Substitute x = 4 into (3) for corresponding value of y

y = 14 - 3(4) = 14 - 12 = 2

solution is (4, 2 )