Can some one explain the step of the following:
1. Graph the system of Inequalities (What will be the points)
y>= -4
x>=5
2. Solve by the substitution method
5x+3y= 7
x=59-7y
3.Graph the equation using the slope and the y-intercept (What are the points)
y= 4/3x+3
Thanks....
1. Graphing the system of inequalities involves plotting the points that satisfy each inequality separately and then shading the region where the two shaded areas overlap.
For the inequality y >= -4, you start by drawing a horizontal line at y = -4. Since the inequality is "greater than or equal to," you should make the line solid. Shade the area above the line to represent all the points where y is greater than or equal to -4.
For the inequality x >= 5, draw a vertical line at x = 5. Again, use a solid line, as the inequality is "greater than or equal to." Shade the region to the right of the line, representing all the points where x is greater than or equal to 5.
The overlapping shaded regions will give you the points that satisfy both inequalities. In this case, the region to the right of the vertical line and above the horizontal line is the solution. The points in this region, including the boundary lines, satisfy both y >= -4 and x >= 5.
2. To solve the given system of equations using the substitution method, follow these steps:
Start with the equations:
5x + 3y = 7 (Equation 1)
x = 59 - 7y (Equation 2)
In equation 2, we have x expressed in terms of y. So, substitute the value of x from equation 2 into equation 1:
5(59 - 7y) + 3y = 7
Simplify the equation:
295 - 35y + 3y = 7
295 - 32y = 7
Now, isolate the variable y:
-32y = 7 - 295
-32y = -288
y = -288 / -32
y = 9
Now that we have the value of y, substitute it back into equation 2 to solve for x:
x = 59 - 7(9)
x = 59 - 63
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 9.
3. To graph the equation y = (4/3)x + 3 using the slope-intercept form, follow these steps:
Start with the equation: y = (4/3)x + 3
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is 4/3 and the y-intercept (b) is 3.
Plot the y-intercept, which is the point (0,3) on the y-axis.
To determine the next points, use the slope. The slope of 4/3 means that for every increase of 3 in the x-coordinate, the y-coordinate increases by 4.
So, starting from the point (0,3), move 3 units to the right on the x-axis and then move 4 units up on the y-axis. This gives you a second point as (3,7).
Connect the two points with a straight line. This line represents all the points that satisfy the equation y = (4/3)x + 3.
You can also find more points by using the slope. For example:
- Move 3 units to the left on the x-axis and then move 4 units down on the y-axis to get (-3,-1).
- Move 6 units to the right on the x-axis and then move 8 units up on the y-axis to get (6,11).
By connecting these points, you can graphically represent the equation y = (4/3)x + 3 on a coordinate plane.