The cost of 3 tacos and a juice is $7. The cost of 4 tacos and 2 juices is $10. If t = the cost of a taco and j = the cost of a juice. What is the cost of one juice and one taco?

t=2

j=1

Step-by-step explanation:

3 tacos and a juice is $7

3t+j=7

4 tacos and 2 juices is $10

4t+2j=10

We have a simultaneous equation. It can be solved either by substitution method or Elimination method. For the purpose of this question, the elimination method will be used

3t+j=7 Equation 1

4t+2j=10 Equation 2

To eliminate j, we multiply Equation 1 by 2, the coefficient of j in equation 2, so that in both equations, j can have the same coefficient.

2 (3t+j=7)

6t+2j=14 Equation 3

We now have

4t+2j=10 Equation 2

6t+2j=14 Equation 3

We subtract equation 2 from equation 3, to eliminate j

6t-4t=2t

2j-2j=0

14-10=4

We have 2t=4

Divide both sides by 2

2t/2=4/2

t=4/2

t=2

Substitute t for 2 in equation 1, to get j

3t+j=7

3 (2) + j=7

6+j=7

j=7-6

j=1

One taco cost $2 while 1 juice cost $2