Question

solve for ( x ) and ( y ) by graphing the system of linear equations. drag the points to move the lines on the graph. then write the solution as an ordered pair. if no solution exists, write
o solution\; if infinite solutions exist, write \infinite solutions\. (\begin{cases} y = \frac{2}{3}x + 1 \\ y = \frac{5}{3}x + 4 end{cases})

Explanation:

Step1: Set equations equal

Since \( y = \frac{2}{3}x + 1 \) and \( y = \frac{5}{3}x + 4 \), set \( \frac{2}{3}x + 1=\frac{5}{3}x + 4 \).

Step2: Solve for \( x \)

Subtract \( \frac{2}{3}x \) from both sides: \( 1=\frac{3}{3}x + 4 \) (simplify \( \frac{5}{3}x-\frac{2}{3}x=\frac{3}{3}x = x \)). Then subtract 4: \( 1 - 4=x \), so \( x=-3 \).

Step3: Find \( y \)

Substitute \( x = - 3 \) into \( y=\frac{2}{3}x + 1 \): \( y=\frac{2}{3}(-3)+1=-2 + 1=-1 \).

Answer:

\((-3, -1)\)