They thought about that when they designed it. So the two signals they transmit are the sum of the L & R channels and the difference of the L & R channels.
A mono reciever ignores the latter and just hears the sum - the two channels added together.
A stereo rcvr adds the two signals (L+R and L-R) to give just the left channel, and it subtracts the two signals (L-R subtracted from L+R) to give just the right channel.
I suppose to be algebraically correct, one ought perhaps to say,
L = 0.5 ( (L+R) + (L-R) )
R = 0.5 ( (L+R) - (L-R) )
The first signal, L+R, was modulated in the normal way, so thats what the mono receiver picks up. So no change was needed in existing receivers.
The second signal (L-R) was modulated onto a sub-carrier at a frequency outside the normal mono pass band, so that mono receivers ignored it. A stereo receiver had a wider passband and processed both signals.