Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.
1 answer:
Answer:
c. The system is inconsistent
Step-by-step explanation:
Multiplying the first equation by 2 gives ...
4x +2y = 4
Compare this to the second equation:
4x +2y = -5
There are no values of x and y that can satisfy both equations. The system is inconsistent.
_____
The equations describe lines that are parallel and do not intersect.
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To solve this, we need to understand Slope Intercept Form (SIF), as well as how to graph a line.
SIF is the standard equation of lines on graphs. It is "y=mx+b" where m is the slope and b is the y-intercept. The y-intercept is the value of y when x is 0.
To find the y-intercept (which we will need to form the equation), we should simply graph the line. This will let us visualize the y-intercept, and overall make it easier to understand.
To graph a line, we should start with the point we have (that being (3, 3)) and follow the slope with rise/run. This means in this case, we will go right 2 for every 1 up, or 2 left for every 1 down.
Below I have attached a graph to help you see how to graph this, which we will get our equation from. The highlighted area is our y-intercept. The red circle shows our original point (3,3), and the blue dots show our slope.
Using the graph, we can see the equation for this line is y=1/2x+1.5.
SIF is the standard equation of lines on graphs. It is "y=mx+b" where m is the slope and b is the y-intercept. The y-intercept is the value of y when x is 0.
To find the y-intercept (which we will need to form the equation), we should simply graph the line. This will let us visualize the y-intercept, and overall make it easier to understand.
To graph a line, we should start with the point we have (that being (3, 3)) and follow the slope with rise/run. This means in this case, we will go right 2 for every 1 up, or 2 left for every 1 down.
Below I have attached a graph to help you see how to graph this, which we will get our equation from. The highlighted area is our y-intercept. The red circle shows our original point (3,3), and the blue dots show our slope.
Using the graph, we can see the equation for this line is y=1/2x+1.5.
we have
see the attached figure to better understand the problem
we know that
The perimeter of the triangle is equal to
and
the area of the triangle is equal to
in this problem
we know that
The distance between two points is equal to
Step
<u>Find the distance AB</u>
Substitute the values in the formula
Step
<u>Find the distance BC</u>
Substitute the values in the formula
Step
<u>Find the distance AC</u>
Substitute the values in the formula
Step
<u>Find the distance DC</u>
Substitute the values in the formula
Step
<u>Find the perimeter of the triangle</u>
substitute the values
therefore
The perimeter of the triangle is equal to
Step
<u>Find the area of the triangle</u>
in this problem
substitute the values
therefore
the area of the triangle is
