Calculate autonomous consumption

Calculate autonomous consumption expenditure from the following data about an economy which is in equilibrium:
National Income = 500
Marginal Propensity to Save = 0.30
Investment expenditure =100

Given, Y = 500,
MPS = 0.30,I = 100, $\overline{C}$ =?
b or MPC = 1- MPS =1-0.30 =0.70
Y = C +I or Y = $\overline{C}$ + bY + I
500 = $\overline{C}$ +0.70x500 +100
500 = $\overline{C}$ +350 +100
$\overline{C}$ = 500 - 450 = 50
Autonomous consumption ($\overline{C}$) = 50