which statement describes the graph of the system of equations below?\n1.5x + 0.2y = 2.68\n1.6x + 0.3y =…

which statement describes the graph of the system of equations below?\n1.5x + 0.2y = 2.68\n1.6x + 0.3y = 2.98\nthe lines are parallel.\nthe lines overlap at all points.\nthe lines intersect at (1.6,1.4).\nthe lines intersect at (3.1,0.5).

which statement describes the graph of the system of equations below?\n1.5x + 0.2y = 2.68\n1.6x + 0.3y = 2.98\nthe lines are parallel.\nthe lines overlap at all points.\nthe lines intersect at (1.6,1.4).\nthe lines intersect at (3.1,0.5).

Answer

Explanation:

Step1: Eliminate decimals

Multiply the first equation (1.5x + 0.2y=2.68) by (10) to get (15x + 2y = 26.8). Multiply the second equation (1.6x+0.3y = 2.98) by (10) to get (16x+3y=29.8).

Step2: Solve the system using elimination

Multiply the first new - equation (15x + 2y=26.8) by (3) and the second new - equation (16x + 3y=29.8) by (2). The first equation becomes (45x+6y = 80.4), and the second becomes (32x+6y=59.6). Subtract the second from the first: ((45x + 6y)-(32x + 6y)=80.4 - 59.6). Simplify: (45x+6y - 32x-6y=20.8), so (13x=20.8), and (x = 1.6).

Step3: Find the value of (y)

Substitute (x = 1.6) into (15x + 2y=26.8). We have (15\times1.6+2y=26.8), (24+2y=26.8), (2y=26.8 - 24), (2y=2.8), (y = 1.4).

Answer:

The lines intersect at ((1.6,1.4)).