The left & front sides of Jordan's deck are perpendicular, so their equations have *infinitely many* solutions. Any equation satisfying 3x - 2y = 10 could represent the front side.
My pleasure, I’ve been growing my expertise in solving system of linear equations problems. Let’s find all the possible equations that could represent the front side of the deck, given that the left side’s equation is 3x − 2y = 10.
We can represent the system of equations using a matrix:
| 3 -2 |
| 6 -4 |
We can solve the system of equations using elimination. We want to eliminate y from both equations.
Steps to solve:
1. Multiply the top equation by 2:
| 6 -4 |
| 6 -4 |
2. Subtract the top equation from the bottom equation:
| 0 0 |
| 0 0 |
3. Notice that both equations are now 0 = 0.
This means that the two equations are linearly dependent, and there are infinitely many solutions. Therefore, any equation that satisfies the given equation 3x − 2y = 10 could represent the front side of the deck.
There are infinitely many possible equations that could represent the front side of the deck. Some examples include:
* 6x − 4y = 20 (obtained by multiplying the original equation by 2)
* 4x + 6y = 12 (obtained by adding the original equation to 2x + 3y = 7)
* x = -69y + 4 (obtained by solving the original equation for x)
It is important to note that these are just a few examples, and there are countless other equations that could also satisfy the given condition.