Question

What is the solution to this matrix equation?[ -1 4 3 2] [x y] = [-26 8] i need to find (x=?) and (y=?)

Answer 1

Answer:

x: $\frac{26}{3y}$

y: $\frac{26}{3x}$

Part A: Finding X

Simplify the equation.

$-4*3*(2xy)=-26*8\\-12*(2xy)=-26*8\\-24*(xy)=-26*8\\-24*xy=-26*8\\-24*xy=-208$

Divide terms.

$\frac{(-24 * (xy))}{-24y}\\\\Cancel~"-24"\\\\\frac{(-24) * xy}{(-24)y} \\= \boxed{\frac{-208}{-24y}}\\\\\\Cancel~"y"\\\\\frac{x(y)}{(y)} = \boxed{\frac{-208}{-24y} }\\x \div 1 = \frac{-208}{-24y}$

Factor -8.

$x = \frac{-8(26)}{-24y}(Cancel~"-8")\\x = \frac{26}{3y}$

Part B: Finding Y

Simplify.

$-4*3*(2xy)=-26*8\\-12*(2xy)=-26*8\\-24*(xy)=-26*8\\-24*xy=-26*8\\-24*xy=-208$

Divide.

$\frac{(-24*(xy))}{-24x} = \frac{-208}{-24x}\\\\Cancel~"-24"\\= \frac{xy}{x} = \frac{-208}{-24x}\\\\Cancel~"x"\\= \frac{-208}{-24x}$

Factor.

$y = \frac{-8(26)}{-24x}\\y = \frac{-8(26)}{-8(3x)} (Cancel -8)\\y = \frac{26}{3x}$