Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. The postal service offers flat-rate shipping for priority mail in special boxes. Today, Irma shipped 1 large box, which cost her $14 to ship. Meanwhile, Britney shipped 6 small boxes and 7 large boxes, and paid $140. How much does it cost to ship these two sizes of box? Shipping costs $_____ for a small box and $_____ for a large box.

Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.  The postal service offers flat-rate shipping for priority mail in special boxes. Today, Irma shipped  1 large box, which cost her $14 to ship. Meanwhile, Britney shipped 6 small boxes and  7 large boxes, and paid $140. How much does it cost to ship these two sizes of box?  Shipping costs $_____ for a small box and  $_____ for a large box.

Bytelearn · Accepted Answer

Set up equations:  Let's set up two equations to represent the costs. Let x be the cost of a small box and y be the cost of a large box. Irma's shipment gives us the equation y = 14. Britney's shipment gives us the equation 6x + 7y = 140. Write system of equations:  Now we'll write the system of equations: 1. y = 14 2. 6x + 7y = 140 Convert to matrix form:  To solve using an augmented matrix, we'll convert the system of equations into matrix form. The matrix will look like this: [0 1 | 14] [6 7 | 140] Eliminate variable y:  We need to use the first equation to eliminate the y variable from the second equation in the matrix. But since the first equation already has y isolated and the coefficient is 1, we can just multiply the first row by -7 and add it to the second row to eliminate y from the second equation. Perform row operation:  After performing the row operation, our matrix should now look like this: [0 1 | 14] [6 0 | 140 - (7 * 14)]

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