Which system is equivalent to y = - 2x, y = x-2?

The given system of equation can be solved if x = 2/3 and y = - 4/3.

So we need to find another system which can be solved by these values.

From the given 4 options lets find out which can be solved by x = 3/2 and y = - 4/3

1.

y = - 2y^2 - 2, x = y - 2

lets put the value of y here

y = - 2 (16/9) - 2 = - 32/9-2 = - 50 / 9

So not an equivalent equation.

2.

y = - 2y^2 + 2, x = y + 2

y = - 2 (16/9) + 2=-32/9+2=-14/9

So not an equivalent system.

3.

y = - 2y^2 - 8y - 8, x = y + 2

y = - 2 (16/9) - 8 (-4/3) - 8 = - 32/9+32/3-8=64/9-8=-8/9

So not an equivalent system.

4.

y = - 2y^2 + 8y - 8, x = y - 2

y = - 2 (16/9) + 8 (-4/3) - 8=-32/9-32/3-8=-128/9-8=-22.22

So this is not an equivalent equation too