System of equations
8th grade
30 points

bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. a month later, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10.

how much does a liter of milk cost, and how much does a loaf of bread cost?

Let x represent the cost of liters of milk
y represent the cost of bread
Next, Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11 means that:
3x+5y=11
Multiply both side by 4
3x(4)+5y(4)=11(4)
12x+20y=44
Then, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10 also means that:
4x+4y=10
Multiply both side by 3
4x(3)+4y(3)=10(3)
12x+12y=30

12x+20y=44
12x+12y=30
Use substitute property
12x+20y=44
-
12x+12y=30
=
8y=14
Divided both side by
8y/8=14/8
y=$1.75/ loaf of bread
3x+5y=11
Substitute y with 1.75
3x+5(1.75)=11
3x+8.75=11
Subtract 8.75 to each side
3x+8.75-8.75=11-8.75
3x=2.25
Divided both side by 3
3x/3=2.25/3
x=$0.75/liter of milk
Check:
3x+5y=11
Substitute x with 0.75 and y with 1.75
3(0.75)+5(1.75)=11
2.25+8.75=11
11=11

4x+4y=10
Substitute x with 0.75 and y with 1.75
4(0.75)+4(1.75)=10
3+7=10
10=10. As a result, a liter of milk cost $0.75 and the cost of bread cost $1.75. Hope it help!