Q: At what point do the lines 5x plus y equals 19 and -x plus 2y equals -6 intersect?

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At the point (2, 4).

It works out that they intersect at: (4, -7)

x = 3 and y = 2 so the lines intersect at the point (3, 2)

Solving the simultaneous equations works out as x = -2 and y = -2 So the lines intersect at: (-2, -2)

Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).

Related questions

At the point (2, 4).

It works out that they intersect at: (4, -7)

By a process of elimination and substitution the lines intersect at: (4, -7)

By a process of elimination and substitution the lines intersect at: (1/4, 0)

x = 1 and y = 6 so the lines intersect at the point (1, 6)

x = 3 and y = 2 so the lines intersect at the point (3, 2)

x = 2 and y = 1 The lines intersect at the point (2, 1)

Solving the simultaneous equations works out as x = -2 and y = -2 So the lines intersect at: (-2, -2)

The lines are perpendicular, and intersect at the point (1.35, 3.55) .

Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).

Two straight lines that intersect.

None. When these two equations are graphed, the two lines are parallel. Since they never intersect, there is no point that satisfies both equations.