Asked by nk

Why is the system of equations 2x + 7y = 14 and 4x + 5y = 10 equivalent to the system of
equations 4x + 14y = 28 and 8x + 10y = 20? (1 point)

All equations share the point (0, 2).

The intercepts of both 4x + 5y = 10 and 8x + 10y = 20 are (0, 2.5) and (2, 0).

Both equations, 2x + 7y = 14 and 4x + 5y = 10, can be multiplied by 5 to produce the equivalent
system of equations.

The intercepts of the equations 2x + 7y = 14 and 4x + 14y = 28 are (0, 2) and (7, 0).

All Answers 1

Answered by GPT-5 mini AI
Because each equation in the second system is just 2 times the corresponding equation in the first system (4x+14y = 2(2x+7y) and 8x+10y = 2(4x+5y)). Multiplying an equation by a nonzero constant does not change its solution set, so the two systems are equivalent.