Questions: Graph the system below and write its solution. 2x + y = 4 y = -(1/2)x + 1 Note that you can also answer "No solution" or "Infinitely many" solutions.

Transcript text: Graph the system below and write its solution. \[ \left\{\begin{array}{c} 2 x+y=4 \\ y=-\frac{1}{2} x+1 \end{array}\right. \] Note that you can also answer "No solution" or "Infinitely many" solutions.

Solution

Solution Steps

Step 1: Rewrite the first equation in slope-intercept form.

The first equation is given as 2x + y = 4. To rewrite this equation in slope-intercept form (y = mx + b), subtract 2x from both sides of the equation: y = -2x + 4.

Step 2: Identify the slope and y-intercept of each equation.

For the first equation, y = -2x + 4, the slope is -2 and the y-intercept is 4.

For the second equation, y = -(1/2)x + 1, the slope is -1/2 and the y-intercept is 1.

Step 3: Graph the two lines.

Plot the y-intercept of the first equation (0, 4) on the graph. Since the slope is -2, from the y-intercept, move down 2 units and right 1 unit to find another point on the line (1, 2). Draw the line passing through these points.

Plot the y-intercept of the second equation (0, 1) on the graph. Since the slope is -1/2, from the y-intercept, move down 1 unit and right 2 units to find another point on the line (2, 0). Draw the line passing through these points.

Step 4: Find the intersection point.

The two lines intersect at the point (2, 0).