Solve by graping the foll:
A. 2X+Y=5
3X-Y=10
B.2X=Y+1
2X-Y=5
I don't know what "graping the foll" is, but problem #2 has no solution, because the lines
Y = 2X -1 (from your fist equation) and
Y = 2x -5 (from your second equation)
never intersect.
gas
To solve these systems of equations by graphing, follow these steps:
A. 2X + Y = 5 and 3X - Y = 10
1. Solve each equation for Y:
2X + Y = 5 -> Y = -2X + 5
3X - Y = 10 -> Y = 3X - 10
Now we have the equations in slope-intercept form (Y = MX + B), where M represents the slope and B represents the y-intercept.
2. Create a graph with a coordinate system and plot the two lines using their slopes and y-intercepts.
For the first equation, Y = -2X + 5, the slope is -2, and the y-intercept is 5. Plot the y-intercept (0, 5) on the graph, and use the slope to find additional points. For example, if you move one unit to the right (X + 1), you move two units down (Y - 2) to get another point (1, 3). Connect these points to draw the line.
For the second equation, Y = 3X - 10, the slope is 3, and the y-intercept is -10. Plot the y-intercept (0, -10) on the graph, and use the slope to find additional points. For example, if you move one unit to the right (X + 1), you move three units up (Y + 3) to get another point (1, -7). Connect these points to draw the line.
3. The solution to the system of equations is the point where the two lines intersect on the graph. In this case, the lines do not intersect, so there is no solution. This means the system of equations is inconsistent.
B. 2X = Y + 1 and 2X - Y = 5
1. Solve each equation for Y:
2X = Y + 1 -> Y = 2X - 1
2X - Y = 5
Now we have one equation in slope-intercept form and another equation where Y is already isolated.
2. Create a graph with a coordinate system and plot the two lines using their slopes and y-intercepts.
For the first equation, Y = 2X - 1, the slope is 2, and the y-intercept is -1. Plot the y-intercept (0, -1) on the graph, and use the slope to find additional points. For example, if you move one unit to the right (X + 1), you move two units up (Y + 2) to get another point (1, 1). Connect these points to draw the line.
For the second equation, 2X - Y = 5, rearrange it as -Y = -2X + 5 and then multiply both sides by -1 to get Y = 2X - 5. The slope is 2, and the y-intercept is -5. Plot the y-intercept (0, -5) on the graph, and use the slope to find additional points. For example, if you move one unit to the right (X + 1), you move two units up (Y + 2) to get another point (1, -3). Connect these points to draw the line.
3. The solution to the system of equations is the point where the two lines intersect on the graph. In this case, the lines do not intersect, so there is no solution. This means the system of equations is inconsistent.