I am surprised that you are not asking this question of your own attorney. In order to retain the house, you would need to pay the trustee the difference between the equity & the exempt amount. Most people in bankruptcy can't pull that kind of money out of thin air, which is a good reason to convert to a Chapter 13 so you can take up to 5 years to pay this money off. Hope this perspective helps!
$75,000 is the CA homestead exemption ($100,000 if there are family members living with you).
What will happen depends on how much additional equity you have. If it's substantial, your case should not have been filed as a Ch7 and you should probably convert to Ch13 if you want to keep the home. If not substantial, the Trustee may just abandon it or possibly work out a deal with you to buy out your equity.
There are two very good answers from attorneys Brian Whitaker and Nancy Bunce. I'll add that to do a successful Chapter 13 to keep your home, you need to have enough monthly income over your expenses to afford to pay the trustee that excess equity (equity above your exemption amount) over five years, plus more if there are other "priority" debts. As said before, you need to discuss this with your own attorney; I'm surprised that you don't seem to understand "lose your home" aspect of filing a Chapter 7 with more equity in your home than can be exempted.
This reply does not constitute legal advice or establish an attorney-client relationship.
If there is equity in the home beyond your $70K exemption then you may very well end up losing your home. The Trustee assigned to your case will most likely look to sell the property. The mortgage(s) against the home would have to be paid and then your exemption would be paid to you, but the rest of the proceeds would be used to pay your various debts. I would strongly suggest you schedule a meeting with your lawyer to discuss the situation in more detail.
I agree with the concern raised by the other answering attorneys. I have no idea if this fits your situation, but sometimes when the equity exceeds the exemption the trustee will still abandon the property because, in addition to the exemption, there are costs involved in liquidating the property. If those costs, added to the exemption, exceed the amount of equity, there is no value to other creditors. The trustee will not liquidate if there is no purpose to be served. The typical cost of sale is in the range of 8% to 10% of the sale price. If the trustee abandons the property, you will keep it as long as you keep the payments current. Even if you could get a line of credit or a refi, why would you? You filed BK to get OUT of debt.