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

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Answer 1 · 2014-08-19T14:58:29

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.