{"id":165050,"date":"2024-11-11T07:01:14","date_gmt":"2024-11-11T07:01:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165050"},"modified":"2024-11-11T07:01:17","modified_gmt":"2024-11-11T07:01:17","slug":"if-the-following-system-of-equations-was-written-as-a-matrix-equation-in-the-form-ax-c-and-matrix-a-was-expressed-in-the-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/11\/if-the-following-system-of-equations-was-written-as-a-matrix-equation-in-the-form-ax-c-and-matrix-a-was-expressed-in-the-form\/","title":{"rendered":"If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form"},"content":{"rendered":"\n

If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

We are given the system of equations:<\/p>\n\n\n\n

[
2x + 8y = 7
]
[
4x – 2y = 9
]<\/p>\n\n\n\n

We are asked to express this system as a matrix equation of the form ( AX = C ), where matrix ( A ) is given by:<\/p>\n\n\n\n

[
A = \\begin{pmatrix} A & C \\ B & D \\end{pmatrix}
]<\/p>\n\n\n\n

Here, we need to match the values of ( A ), ( B ), ( C ), and ( D ) from the system of equations, and then find the value of ( a – b + c + d ).<\/p>\n\n\n\n

Step 1: Write the system as a matrix equation<\/h3>\n\n\n\n

The system of equations can be written as:<\/p>\n\n\n\n

[
\\begin{pmatrix} 2 & 8 \\ 4 & -2 \\end{pmatrix} \\begin{pmatrix} x \\ y \\end{pmatrix} = \\begin{pmatrix} 7 \\ 9 \\end{pmatrix}
]<\/p>\n\n\n\n

This corresponds to the general matrix equation ( AX = C ), where:<\/p>\n\n\n\n