Question

How do I use matrices to find the solution of the system of equations `3x+4y=10` and `x-y=1`?

Answer 1

3 ways, Cramer's Rule, Elimination, or Substitution. Let's look at Cramer's rule below:

Standard equation `1 = ax + by = c` and Standard equation `2 = dx + ey = f`

Therefore:
`a = 3, b = 4, c = 10, d = 1, e = -1, f = 1`

Step 1, calculate the denominator Delta (`Delta`):

`Delta = a * e - b * d`
`Delta = (3 * -1) - (4 * 1)`
`Delta = -3 - 4`
`Delta = -7`

Step 2, calculate the numerator for `x`:

`N_x = c * e - b * f`
`N_x = (10 * -1) - (4 * 1)`
`N_x = -10 - 4`
`N_x = -14`

Step 3, calculate the numerator for `y`:

`N_y = a * f - c * d`
`N_y = (3 * 1) - (10 * 1)`
`N_y = 3 - 10`
`N_y = -7`

Now we have all of our components. Evaluate and solve:

`x = N_x/Delta`

`x = -14/-7`

`x = 2`

`y = N_y/Delta`

`y = -7/-7`

`y = 1`

For calculator help with similar problems, check out the 2 unknowns calculator

Just wanted to mention that `Delta, N_x, N_y` are called determinants, in case anyone wants to look up more info about matrices.