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# Equations in several variables in practice - The linear case

Solving exercises about systems of equations

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.)

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