Find a solution of equations by graphing Y = 3X - 1
-3X +Y =-2
4,11
1,11
No solution
Infinitely many solutions
To find the solution of the system of equations by graphing, we need to plot the equations on a graph and see where they intersect.
First, let's graph the equation Y = 3X - 1:
Plotting a few points, we have:
X = 0, Y = -1
X = 1, Y = 2
X = -1, Y = -4
We can draw a straight line passing through these points.
Next, let's graph the equation -3X + Y = -2:
Rewriting the equation in slope-intercept form, we get:
Y = 3X - 2
Plotting a few points, we have:
X = 0, Y = -2
X = 1, Y = 1
X = -1, Y = -5
We can draw a straight line passing through these points.
Now, let's locate the point of intersection between these two lines. From the graph, we can see that the two lines intersect at the point (1, 2).
Therefore, the solution to the system of equations is X = 1 and Y = 2.
To find a solution of the equations by graphing, we will plot the lines represented by the equations and find the point (if any) where they intersect.
The first equation is given as Y = 3X - 1. To plot this line, we will find some points that satisfy this equation.
Let's choose X = 0. Substituting this into the equation, we get Y = 3(0) - 1 = -1. Thus, one point on the line is (0, -1).
Let's choose X = 1. Substituting this into the equation, we get Y = 3(1) - 1 = 2. Thus, another point on the line is (1, 2).
Plot these points and draw a line through them.
The second equation is given as -3X + Y = -2. To plot this line, we will also find some points that satisfy this equation.
Let's choose X = 0. Substituting this into the equation, we get -3(0) + Y = -2, which simplifies to Y = -2. Thus, one point on the line is (0, -2).
Let's choose X = 1. Substituting this into the equation, we get -3(1) + Y = -2, which simplifies to Y = 1. Thus, another point on the line is (1, 1).
Plot these points and draw a line through them.
Now, we can observe the graph and see if the lines intersect at any point.
Based on the given points (4, 11) and (1, 11), if we compare the Y-coordinates, we can see that the Y-coordinate is the same, while the X-coordinates are different. This means that the lines are parallel and do not intersect.
Since the lines do not intersect, there is no solution to the system of equations. Therefore, the correct answer is "No solution."