Math

QuestionSolve the system:
(4398)(xy)=(611) \begin{pmatrix} 4 & 3 \\ 9 & 8 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 6 \\ 11 \end{pmatrix}

Studdy Solution

STEP 1

Assumptions1. The given system of equations is represented in matrix form. . The system of equations is linear.
3. The system of equations has a unique solution.

STEP 2

The given matrix equation can be written as a system of linear equations. The first equation is obtained by multiplying the first row of the matrix by the column vector, and the second equation is obtained by multiplying the second row of the matrix by the column vector.
4x+y=64x +y =69x+8y=119x +8y =11

STEP 3

We can solve this system of equations using substitution or elimination. Here, we will use elimination. Multiply the first equation by8 and the second equation by3 to make the coefficients of y the same in both equations.
32x+24y=4832x +24y =4827x+24y=3327x +24y =33

STEP 4

Subtract the second equation from the first to eliminate y.
32x27x=483332x -27x =48 -33

STEP 5

implify the equation to find the value of x.
5x=155x =15x=15/5x =15 /5x=3x =3

STEP 6

Substitute x =3 into the first equation to find the value of y.
43+3y=64*3 +3y =6

STEP 7

implify the equation to find the value of y.
12+3y=612 +3y =63y=6123y =6 -123y=63y = -6y=6/3y = -6 /3y=2y = -2The solution to the system of equations is x =3, y = -2.

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