It's hard to imagine that you can misconstrue something as badly as you do here, yet you can read road signs well enough that some state somewhere has granted you a driver's license (but that's govmint for ya). Better than I have shown that you're all wet in your reading of Hodge. I could sooner teach my dog to read.I'll allow Charles Hodge take you to school on that:
Every man is required to satisfy the demands of the law. No man is required to do either more or less. If those demands are satisfied by a representative or substitute, his work is equally available for all. The secret purpose of God in providing such a substitute for man, has nothing to do with the nature of his work, or with its appropriateness. The righteousness of Christ being of infinite value or merit, and being in its nature precisely what all men need, may be offered to all men. It is thus offered to the elect and to the non-elect; and it is offered to both classes conditionally. That condition is a cordial acceptance of it as the only ground of justification. If any of the elect (being adults) fail thus to accept of it, they perish. If any of the non-elect should believe, they would be saved. What more does any Anti-Augustinian scheme provide? The advocates of such schemes say, that the design of the work of Christ was to render the salvation of all men possible. All they can mean by this is, that if any man (elect or non-elect) believes, he shall, on the ground of what Christ has done, be certainly saved. But Augustinians say the same thing. It teaches that God in effecting the salvation of his own people, did whatever was necessary for the salvation of all men, and therefore to all the offer may be, and in fact is made in the gospel. ... Christ, therefore, did not die equally for all men. He laid down his life for his sheep; He gave Himself for his Church. But in perfect consistency with this, He did all that was necessary, so far as a satisfaction to justice is concerned, all that is required for the salvation of all men. So that all Augustinians can join with the Synod of Dort in saying, 'No man perishes for want of an atonement.'
But even so, who cares about Hodge? I appeal to the true Schoolmaster. The law. And you will not find Egypt represented on the Day of Atonement. No aspect of the offering is effectual for them, whether it's the satisfaction of the law, nor the forgiveness of their sins.