Outside the high school program / Cartesian equations 4 exercises (100% corrected)

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1. Lines: intersection E.2952 In the plane provided with an orthonormal reference frame O ; I ; J , consider the two straight lines ( d 1 ) and ( d 2 ) with Cartesian equations : ( d 1 ) : 2 x − y + 1 = 0 ; ( d 2 ) : x − 3 y − 4 = 0 1 Are the straight lines ( d 1 ) and ( d 2 ) parallel? 2 Determine the coordinates of the point of intersection. E.9832 In the plane provided with a reference frame, consider the two straight lines (Δ) and (Δ ) of Carte-sian equation : (Δ) : 5 x − 2 y + 2 = 0 ; (Δ ) : x + y − 1 = 0 1 Justify that the straight lines (Δ) and (Δ ) are not par-allel. 2 Determine the coordinates of the point of intersection of these two straight lines. E.9833 In the plane provided with a reference frame, consider the two straight lines ( d ) and ( d ) admit as Cartesian equation : ( d ) : 7 x + 4 y − 1 = 0 ; ( d ) : − 3 x + y − 5 = 0 1 Justify that the straight lines ( d ) and ( d ) are secant. 2 a Solve the system : ( S ) : 7 x + 4 y − 1 = 0 − 3 x + y − 5 = 0 b Interpret graphically the set of solutions of the previ-ous system. E.5337 Consider the plane provided with a O ; −→ i ; −→ j and the straight lines ( d 1 ) and ( d 2 ) defined by the Cartesian equations : ( d 1 ): 4 x − 6 y + 2 = 0 ; ( d 2 ): x + 2 y − 3 = 0 Justify that the straight lines ( d 1 ) and ( d 2 ) are secant, then determine the coordinates of their point of intersection. https://chingmath.fr chapExoCorrec/2952 sacados/2952 chapExoCorrec/9832 sacados/9832 chapExoCorrec/9833 sacados/9833 chapExoCorrec/5337 sacados/5337