Write as a Vector Equality -3x-4y=2 , 8y=-6x-4

Problem

−3*x−4*y=2,8*y=−6*x−4

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables x and y are on the left side and the constants are on the right.

2. Rewrite the first equation:

−3*x−4*y=2

3. Rewrite the second equation by adding 6*x to both sides:

6*x+8*y=−4

4. Identify the coefficients of x and y to form the coefficient matrix and the constant vector.

5. Express the system as a linear combination of vectors by separating the x and y components.

x*([−3],[6])+y*([−4],[8])=([2],[−4])

Final Answer

x*([−3],[6])+y*([−4],[8])=([2],[−4])

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