Question

drag the system of equation to the point that represents the solution to the system.
3x + 2y = 10
6x - y = 10

y = 3x - 7
y = 2x - 5

y = 6
x = -5

4x - 3y = 5
3x + 2y = -9

2x - y = -13
y = x + 9

x + y = 7
x - y = -1

Explanation:

Step1: Solve the system \(

$$\begin{cases} 4x - 3y = 5 \\ 3x + 2y = -9 \end{cases}$$

\)
Multiply the first equation by 2: \( 8x - 6y = 10 \)
Multiply the second equation by 3: \( 9x + 6y = -27 \)
Add the two equations: \( 8x - 6y + 9x + 6y = 10 + (-27) \)
Simplify: \( 17x = -17 \), so \( x = -1 \)
Substitute \( x = -1 \) into \( 4x - 3y = 5 \): \( 4(-1) - 3y = 5 \)
Simplify: \( -4 - 3y = 5 \), \( -3y = 9 \), \( y = -3 \)

Step2: Identify the point with \( x = -1 \), \( y = -3 \)

From the graph, the point at \( x = -1 \), \( y = -3 \) is the one at (-1, -3) (the purple dot at x=-1, y=-3).

Answer:

Drag the system \(

$$\begin{cases} 4x - 3y = 5 \\ 3x + 2y = -9 \end{cases}$$

\) to the point (-1, -3) (the purple dot at x = -1, y = -3 on the graph).