How do you solve the system 3x-5y=-24, 5x+4y=-3 using matrix equation? Precalculus Matrix Row Operations Solving a System of Equations Using a Matrix 1 Answer Eddie Feb 14, 2017 ((x),(y)) = ((-3),(3)) Explanation: A mathbf x = mathbf b implies ((3, -5),(5,4))((x),(y)) = ((-24),(-3)) Here: A^(-1) = ((3, -5),(5,4))^(-1) = 1/(3*4 - 5*(-5)) ((4, 5),(-5,3)) = 1/(37) ((4, 5),(-5,3)) So we can say that: 1/(37) ((4, 5),(-5,3))((3, -5),(5,4))((x),(y)) =1/(37) ((4, 5),(-5,3)) ((-24),(-3)) implies ((1, 0),(0,1))((x),(y)) =1/(37) ((4, 5),(-5,3)) ((-24),(-3)) implies ((x),(y)) = 1/37 ((-111),(111)) = ((-3),(3)) Answer link Related questions How do I use matrices to solve the system 2x+3y=4 and 5x+8y=11? How do I solve a system of equations using an augmented matrix? How do I solve a system of 3 equations with a matrix? How do I solve a system of equations using inverse matrices? How do I solve a system of 2 equations using a matrix? How do I use matrices to find the solution of the system of equations 3x+4y=10 and x-y=1? How do I use matrices to find the solution of the system of equations c+3d=8 and c=4d-6? How do I use matrices to find the solution of the system of equations y=1/3x+7/3 and y=−5/4x+11/4? How do I use matrices to find the solution of the system of equations y=−2x+4 and y=−2x−3? How do I use matrices to find the solution of the system of equations y=−2x−4 and y+4=−2x? See all questions in Solving a System of Equations Using a Matrix Impact of this question 2078 views around the world You can reuse this answer Creative Commons License