which is the approximate solution to the system y = 0.5x + 3.5 and y = -\\frac{2}{3}x + \\frac{1}{3} shown…

which is the approximate solution to the system y = 0.5x + 3.5 and y = -\\frac{2}{3}x + \\frac{1}{3} shown on the graph?\n(-2.7, 2.1)\n(-2.1, 2.7)\n(2.1, 2.7)\n(2.7, 2.1)

which is the approximate solution to the system y = 0.5x + 3.5 and y = -\\frac{2}{3}x + \\frac{1}{3} shown on the graph?\n(-2.7, 2.1)\n(-2.1, 2.7)\n(2.1, 2.7)\n(2.7, 2.1)

Answer

Explanation:

Step1: Set the two equations equal.

Since $y$ is equal in both equations, we set $0.5x + 3.5=-\frac{2}{3}x+\frac{1}{3}$. First, convert $0.5=\frac{1}{2}$. The equation becomes $\frac{1}{2}x + 3.5=-\frac{2}{3}x+\frac{1}{3}$. Multiply through by 6 to clear the fractions: $6\times\frac{1}{2}x+6\times3.5 = 6\times(-\frac{2}{3}x)+6\times\frac{1}{3}$, which simplifies to $3x + 21=-4x + 2$.

Step2: Solve for $x$.

Add $4x$ to both sides: $3x+4x + 21=-4x+4x + 2$, so $7x+21 = 2$. Then subtract 21 from both sides: $7x+21 - 21=2 - 21$, getting $7x=-19$. Divide both sides by 7: $x=\frac{-19}{7}\approx - 2.7$.

Step3: Solve for $y$.

Substitute $x\approx - 2.7$ into $y = 0.5x+3.5$. Then $y=0.5\times(-2.7)+3.5=-1.35 + 3.5 = 2.15\approx2.1$.

Answer:

A. $(-2.7,2.1)$