Large tank: 6 liters, small tank: 3 liters. See solution.
Practice makes perfect
We want to find the volume of each size of tank used by a laboratory to store liquid nitrogen. To do so, we will create a system of linear equations and then solve it using the Elimination Method. Let's use x to represent the volume of the large tank and y to represent the volume of the small tank.
Volume of the large tank - x Volume of the small tank - y
From the exercise we know that the combined volume of 3 large tanks and 2 small tanks is 24 liters. Let's write this fact as an equation.
3* x+ 2* y= 24We also know that the combined volume of 2 large tanks and 3 small tanks is 21 liters.
2* x+ 3* y= 21
Now that we have created two equations, we can combine them into a system of equations.
3x+2y=24 & (I) 2x+3y=21 & (II)
We are ready to solve this system to find the volumes of the tanks. Notice that no pair of like terms has the same or opposite coefficients. Let's multiply Equation (I) by 3 and Equation (II) by 2 so that the y-terms will have the same coefficient.
Now we can subtract Equation (II) from Equation (I) to get an equation in only one variable, x. We also could have multiplied one of the equations by a negative number and then added them — the answer would be the same.
