Equations in several variables in practice - The linear case

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Solve the system (quadleftlbrace begin{array}{l} 5x+3y = 2 x+2y= -5 end{array} right.)

Exercise. 2 [Solved only in the PDF file]

Solve the following systems:

i) (quadleftlbrace begin{array}{l} x-2y = 3 4x-8y = 12 end{array} right.)

ii) (quadleftlbrace begin{array}{l} x-2y = 1 -2x+4y = 5 end{array} right.)

Ex 3. [Solved only in the PDF file]

Discuss the value of the parameter (hinmathbb{R}) in such a way that the following systems of polynomial equations of degree 1 in the unknowns (x), (y) admit one solution, infinite solutions, no solutions.

i) (quadleftlbrace begin{array}{l} hx+y = 1 x-y = 2 end{array} right.)

ii) (quadleftlbrace begin{array}{l} x+y = 6 x+hy = 2h end{array} right.)