Question

При каких значениях параметра a прямые 5x-2y=3 и x+y=a перемекаются в точке, принадлежащей оси Oy.

Answer 1

Так как точка лежит на оси oy, то ее x координата равна 0
можно составить систему:
5x-2y=3
x+y=a
x=0
решаем:
-2y=3
y=-1,5
y=a
a=-1,5
Ответ: при a=-1,5

Answer 2

Finding the Intersection Point of Two Lines

To find the values of the parameter a for which the lines 5x - 2y = 3 and x + y = a intersect at a point on the y-axis, we can use the fact that the y-coordinate of any point on the y-axis is 0. By substituting y = 0 into the equations of the lines, we can solve for the corresponding x-coordinates.

The intersection point of the two lines lies on the y-axis when the x-coordinate is not equal to 0. This occurs when the lines intersect at a point other than the origin.

Let's proceed with the calculations.

Calculating the Intersection Point

For the line 5x - 2y = 3: - Substituting y = 0, we get: 5x = 3. - Solving for x, we find: x = 3/5.

For the line x + y = a: - Substituting y = 0, we get: x = a.

Therefore, the lines intersect at a point on the y-axis when a = 3/5.

Conclusion

The value of the parameter a for which the lines 5x - 2y = 3 and x + y = a intersect at a point on the y-axis is a = 3/5. This means that when a = 3/5, the lines intersect at a point on the y-axis, specifically at the point where x = 3/5 and y = 0.