how do i do these problems????
Graph each pair of equations in the same coordinate plane. Find the coordinates of the point where the graphs intersect. Then show by substitution that the coordinate satisfy both equations.
1. 2x + 5=0
2x + y=8
Graph each equation
2. y=|x|
HELP!!! :[
(1.) first, graph the equations,, there are various ways how to graph them,, for linear equations, i usually get the x- and y- intercept (*x- and y- intercepts are points*):
*note: to get x-intercept, set y=0 and solve for x,, to get y-intercept, set x=0 and solve for y,,
>>in the 1st equation, 2x + 5=0, since there is no variable y, just solve for x and you'll get x=-5/2. the graph of x=-5/2 is a vertical line passing through -5/2 (or -2.5)
*another note: this equation has no y-intercept since there is no value of y in which x will be zero (that is, the graph of x=-5/2 will never pass the y-axis)
>>in the 2nd equation, 2x + y=8, to get x-intercept, set y=0, so:
2x + (0) = 8 *solve for x
x=4
therefore, x-int: (4,0)
for the y-intercept, set x=0, so:
2(0) + y = 8 *solve for y
y=8
therefore, y-int: (0,8)
plot (4,0) and (0,8) on the same cartesian plane and connect, and extend the line,, this is now the graph of the 2nd equation,,
>>now, locate the point of intersection~
*to check if it's really the point of intersection, do substitution,, to do this, choose one of the equations, and express one variable in terms of the other variable,, in this case we choose the 1st equation since it readily gives the value of x which is -5/2,,
not substitute this to the 2nd equation:
2(-5/2) + y = 8
y=13
>>thus, the point of intersection is at (-5/2, 13)
(2.) graph y=|x|
*to do this, first, graph y=x (the version which does not contain the absolute value),, now, since y=|x| means y is restricted only to positive values, look for the area in the graph in which y is negative (it's in 3rd quadrant, isn't it),, then make a "mirror image" of this in the 2nd quadrant (2nd quadrant, because y values are positive in there),, thus its graph should be V-shaped,,
so there,, =)
sorry for long explanation..
Step 1: Graphing the equations and finding the point of intersection
For the first problem: 2x + 5 = 0 and 2x + y = 8
To graph the first equation, 2x + 5 = 0, we can start by solving for x. Subtract 5 from both sides of the equation:
2x = -5
Divide both sides by 2:
x = -5/2
So the x-coordinate for the point of intersection is -5/2. Now we can substitute this value into the second equation, 2x + y = 8, to find the y-coordinate:
2(-5/2) + y = 8
-5 + y = 8
y = 8 + 5
y = 13
Hence, the coordinates of the point where the graphs intersect are (-5/2, 13).
For the second problem: y = |x|
The equation y = |x| represents a V-shaped graph. Notice that whenever x is positive or zero, y will be equal to x. And whenever x is negative, y will be equal to -x. You can choose a few x-values and find the corresponding y-values to plot your graph.
Step 2: Graphing each equation
For the first problem, graph the equations 2x + 5 = 0 and 2x + y = 8 on the same coordinate plane.
For the second problem, graph the equation y = |x| on a coordinate plane.
Please let me know if you need help with any specific steps in graphing these equations!
To solve these problems, you can follow these steps:
1. Graphing Equations:
a. For the first problem, you have two equations: 2x + 5 = 0 and 2x + y = 8. To graph them, you need to first solve each equation for y in terms of x.
- For the first equation, 2x + 5 = 0, subtract 5 from both sides to get 2x = -5, and then divide both sides by 2 to get x = -5/2. This equation represents a vertical line passing through the point (-5/2, 0) on the coordinate plane.
- For the second equation, 2x + y = 8, subtract 2x from both sides to get y = -2x + 8. This equation represents a line with a slope of -2 and a y-intercept of 8.
b. Plot the points (-5/2, 0) and (0, 8) on the coordinate plane and draw the lines representing the equations.
c. The point where the two lines intersect is the solution to the system of equations.
2. Substitution:
a. Once you have the point of intersection, you can substitute its coordinates back into the original equations to verify that they satisfy both equations.
b. For example, in the first problem, if the point of intersection is (2, 4), substitute these values into the equations and check if they hold true.
Regarding the second problem, graphing the equation "y = |x|" involves plotting points that satisfy the equation, taking into account the absolute value function.
a. Start by choosing x values and finding the corresponding y values.
- For example, when x = -3, y = |-3| = 3. When x = 0, y = |0| = 0.
b. Plot these points on the coordinate plane and connect them with a smooth curve. The graph of y = |x| is V-shaped, with the vertex at (0, 0).
c. There are no specific points of intersection to find or use substitution for in this problem.
Remember, practicing graphing and solving equations will help you develop your understanding and skills in these areas.