Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Roscoe has punch cards for his favorite tea house and his favorite coffee shop. He currently has 7 punches on the tea punch card and 10 punches on the coffee punch card. Given his regular routine, he consistently earns 7 new punches per week on the tea punch card and 6 on the coffee punch card. Before too long, Roscoe will have the same number of punches on each card. How many punches will Roscoe have on each card? How long will that take?

Roscoe will havepunches on each card in weeks.

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!

Point is the only one not undefined