which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98…

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).

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

Explanation:

Step1: Multiply equations to eliminate y

Multiply the first - equation $1.5x + 0.2y=2.68$ by 3 and the second - equation $1.6x + 0.3y = 2.98$ by 2. The first equation becomes $4.5x+0.6y = 8.04$ and the second equation becomes $3.2x+0.6y = 5.96$.

Step2: Subtract the second new - equation from the first new - equation

$(4.5x + 0.6y)-(3.2x + 0.6y)=8.04 - 5.96$. Simplify to get $4.5x+0.6y - 3.2x - 0.6y=2.08$, then $1.3x=2.08$. Solve for $x$: $x=\frac{2.08}{1.3}=1.6$.

Step3: Substitute $x = 1.6$ into the first original equation

Substitute $x = 1.6$ into $1.5x+0.2y = 2.68$. We have $1.5\times1.6+0.2y = 2.68$. $2.4+0.2y = 2.68$. Subtract 2.4 from both sides: $0.2y=2.68 - 2.4=0.28$. Solve for $y$: $y=\frac{0.28}{0.2}=1.4$.

Answer:

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