Question
Determine if the system of equations has a solution
by graphing.
𝑦 = −2𝑥 + 7
𝑦 = −
3
2
𝑥 + 6
by graphing.
𝑦 = −2𝑥 + 7
𝑦 = −
3
2
𝑥 + 6
Answers
GPT 3.5
To determine if the system of equations has a solution by graphing, we first graph both equations on the same set of axes.
For the first equation y = -2x + 7, plot the y-intercept at (0,7) and then use the slope of -2 to plot another point. For example, if we move one unit to the right (increase x by 1), we would move down 2 units (decrease y by 2) to get the point (1,5).
For the second equation y = -3/2x + 6, plot the y-intercept at (0,6) and then use the slope of -3/2 to plot another point. For example, if we move two units to the right (increase x by 2), we would move down 3 units (decrease y by 3) to get the point (2,3).
Next, connect the points for each equation with a straight line:
Equation 1: y = -2x + 7
Equation 2: y = -3/2x + 6
After graphing the two equations, we can see that the lines are parallel and do not intersect. This means that the system of equations does not have a solution because the lines never meet.
For the first equation y = -2x + 7, plot the y-intercept at (0,7) and then use the slope of -2 to plot another point. For example, if we move one unit to the right (increase x by 1), we would move down 2 units (decrease y by 2) to get the point (1,5).
For the second equation y = -3/2x + 6, plot the y-intercept at (0,6) and then use the slope of -3/2 to plot another point. For example, if we move two units to the right (increase x by 2), we would move down 3 units (decrease y by 3) to get the point (2,3).
Next, connect the points for each equation with a straight line:
Equation 1: y = -2x + 7
Equation 2: y = -3/2x + 6
After graphing the two equations, we can see that the lines are parallel and do not intersect. This means that the system of equations does not have a solution because the lines never meet.