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

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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 $1 = a x + b y = c$ $1 = ax + by = c$ and Standard equation $2 = d x + e y = f$ $2 = dx + ey = f$

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

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.

How do I use matrices to find the solution of the system of equations 3x+4y=103x+4y=103x+4y=10 and x-y=1x−y=1x-y=1?