Burger Joint is celebrating their grand opening. For 2 milkshakes and 3 burgers, the cost is $13. For 5milkshakes and 7 burgers, the cost is $31.What is the cost of 1 burger and 1 milkshake?

For this case we propose a system of equations:x: Let the variable representing the cost of a milkshakey: Let the variable representing the cost of a burgerAccording to the statement we have:[tex]2x + 3y = 13\\5x + 7y = 31[/tex]We multiply the first equation by -5:[tex]-10x-15y = -65[/tex]We multiply the second equation by 2:[tex]10x + 14y = 62[/tex]We have the following equivalent system:[tex]-10x-15y = -65\\10x + 14y = 62[/tex]We add the equations:[tex]-10x + 10x-15y + 14y = -65 + 62\\-y = -3\\y = 3[/tex]Thus, the cost of a burger is $3.[tex]2x + 3 (3) = 13\\2x + 9 = 13\\2x = 13-9\\2x = 4\\x = \frac {4} {2}\\x = 2[/tex]So, the cost of a milkshake is $2Answer:Burger: $3Milkshake: $2