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
