Final answer:
To solve the system of equations -2x - 3y = -26 and 3x + 4y = 36 using a matrix, we can write the system in matrix form and find the solution by multiplying both sides by the inverse of the coefficient matrix. The solution as an ordered pair (x, y) is (16, -20).
Step-by-step explanation:
To solve the system of equations using a matrix, we can write the system in matrix form:
[ -2 -3 ] [ x ] = [ -26 ]
[ 3 4 ] [ y ] = [ 36 ]
To find the solution, we can use matrix inversion. Multiply both sides of the equation by the inverse of the coefficient matrix:
[ x ] = [ -2 -3 ]-1[ -26 ]
[ y ] = [ 3 4 ]-1[ 36 ]
Calculating the inverse:
[ -2 -3 ]-1 = [ -4/3 -2/3 ]
[ 3 4 ]-1 = [ 4/3 -1/3 ]
Finally, substitute the values of x and y back into the system to find the solution:
x = (-4/3)(-26) + (-2/3)(36) = -8 + 24 = 16
y = (4/3)(-26) + (-1/3)(36) = -32 + 12 = -20
Therefore, the solution as an ordered pair (x, y) is (16, -20).