We have 2 unknowns, so that means we need to have 2 equations to find them.
Let r=cost of a ribeye dinner
s=cost of a salmon dinner
Eq. I: 13r+26s=597.19
Eq. II: 25r+13s=581.85
Use the elimination method to solve for r by multiplying Eq. II by 2 then subtracting Eq. I from Eq. II:
2 X Eq. II=50r+26s=1163.70 Eq. II multiplied by 2
-(13r+26s= 597.19) Eq. I
r=566.51/37 divide both sides by 37
Use this value for r in either equation to find the value for s.
13r+26s=597.19 Eq. I
13(15.31)+26s=597.19 substituting for r
26s=597.19-199.03 subtract 199.03 from both sides
s=398.16/26 divide both sides by 26
Therefore, both dinners cost roughly $15.31.