Question

Twice one number plus a second number is 42 and the first number is 4 more than 3 times the second

Answer 1

Answer / Step-By-Step Explanation:

"Twice one number plus a second number is 42."

2x + y = 42

y = -2x + 42

"The first number is 4 more than 3 times the second."

x - y = -6

x - (-2x + 42) = -6

x + 2x - 42 = -6

3x = 36

First number: x = 12

Second Number: y = -2 (12) + 42 = -24 + 42 = 18

2 × 12 + 18 = 42

(24 + 18 = 42)

Hope this helps!

Answer 2

x = 130/7, y = 34/7

Explanation:

Let x = the first number

and y = the second number

Then

(1) 2x + y = 42

(2) x = 3y + 4

Subtract 3y from each side of (2) (3) x - 3y = 4

Multiply Equation (3) by 2 (4) 2x - 6y = 8

Subtract (4) from (1) 7y = 34

Divide each side by 7 (5) y = 34/7

Substitute (5) into (1) 2x + 34/7 = 42

Subtract 34/7 from each side 2x = 42 - 34/7

Simplify 2x = 260/7

Divide each side by 2 x = 130/7

x = 130/7, y = 34/7

Check:

(1) 2(130/7) + 34/7 = 42 (2) 130/7 = 3(34/7) + 4

260/7 + 34/7 = 42 130/7 = 102 /7 + 28/7

294/7 = 42 130/7 = 130/7

42 = 42