Question

SHOW WORK!! solve
y = 3x + 2
6x – 2y = 10

Answer 1

No solution.

Explanation:

Replace y in the second equation with what it equals in the first equation.

6x - 2(3x + 2) = 10.

6x - 6x - 4 = 10.

-4 doesn't equal 10 so x has no solution, and thus y also has no solution.

Answer 2

Answer: The solution set is empty.

Explanation:

Express the equations as

f(x,y) = 0 and g(x,y) = 0.

3x - y + 2 = 0 and 6x - 2y - 10 = 0

divide second equation by 2.

3x - y + 2 = 0 and 3x - y - 5 = 0

Subtract the equations, and you get "False", as 7 is not zero.

This means there are no pairs (x,y) which satisfy both equations. The graphs of the equations do not intersect. In fact, they are both lines with slope 3, and y intercept either -2 or 5. Lines with equal slope are either the same line, or they are parallel. Parallel lines on the flat plane do not intersect.