Question

Which statement describes the graph of the system of equations below?

1.5x + 0.2y = 2.68

1.6x + 0.3y = 2.98

The lines are parallel.
The lines overlap at all points.
The lines intersect at (1.6,1.4).
The lines intersect at (3.1,0.5).

Answer 1

Solve by elimination. Multiply the first equation by 3 and the second by 2:

4.5x + 0.6y = 8.04
3.2x + 0.6y = 5.96

Subtract the second from the first: 1.3x = 2.08, so x = 1.6. Substitute into 1.5x + 0.2y = 2.68:

1.5(1.6) + 0.2y = 2.68 → 2.4 + 0.2y = 2.68 → 0.2y = 0.28 → y = 1.4.

The lines intersect at (1.6, 1.4).