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

##### 1 Answer

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

Standard equation

Therefore:

Step 1, calculate the denominator Delta (

#Delta = a * e - b * d#

#Delta = (3 * -1) - (4 * 1)#

#Delta = -3 - 4#

#Delta = -7#

Step 2, calculate the numerator for

#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

#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#

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