Questions: Solve each system by graphing. 1) y=-3x+4 y=3x-2

Transcript text: Solve each system by graphing. 1) \[ \begin{array}{l} y=-3 x+4 \\ y=3 x-2 \end{array} \]

Solution

Solution Steps

Step 1: Graph the first equation

The first equation is \(y = -3x + 4\). This is in slope-intercept form (\(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept. In this case, the slope is -3 and the y-intercept is 4. Plot the y-intercept (0, 4) on the graph. Since the slope is -3, which can be written as \(-3/1\), from the y-intercept, go down 3 units and right 1 unit to plot another point (1, 1). Draw a line through these two points.

Step 2: Graph the second equation

The second equation is \(y = 3x - 2\). This is also in slope-intercept form. The slope is 3 and the y-intercept is -2. Plot the y-intercept (0, -2) on the graph. Since the slope is 3, which can be written as \(3/1\), from the y-intercept, go up 3 units and right 1 unit to plot another point (1, 1). Draw a line through these two points.

Step 3: Find the intersection point

The solution to the system of equations is the point where the two lines intersect. In this case, the lines intersect at the point (1, 1).