Question

Graph this system of equations on the coordinate plane:

y = -3x + 3
y = (1/2)x - 4
Use the Mark Feature tool to indicate the solution to the system on the graph.

Answer 1

The solution to the system of equations is the point of intersection on the graph of y = -3x + 3 and
`\( y = (1)/(2)x - 4 \)`. Marking the point of intersection, the solution is (2, -3).

Step-by-step explanation:

To find the solution to the system of equations, we need to graph the two equations y = -3x + 3 and
`\( y = (1)/(2)x - 4 \)` on the coordinate plane. The point of intersection on the graph represents the solution to the system.

Firstly, consider the equation y = -3x + 3. To graph this linear equation, identify the y-intercept at (0, 3) and use the slope of -3 to find another point, creating a straight line on the coordinate plane.

Secondly, consider the equation
`\( y = (1)/(2)x - 4 \).` Find the y-intercept at (0, -4) and use the slope of
`\((1)/(2)\)` to graph the second line.

The point of intersection between these two lines on the graph represents the solution to the system of equations. In this case, the solution is the point (2, -3). To further confirm this, substitute x = 2 into either equation to find the corresponding y-value. Plugging x = 2 into y = -3x + 3 yields y = -3(2) + 3 = -3 , confirming that the solution is indeed (2, -3).

By using the Mark Feature tool, highlight the point (2, -3) on the graph to clearly indicate the solution to the system of equations. This ensures a visual representation of the mathematical solution.