Answer:
Please check the attached graph.
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given the system of equations
2x - 5y = -5 --- [Equation 1]
y = -3x + 1 --- [Equation 2]
converting the equation 1 in the slope-intercept form
2x - 5y = -5
5y = 2x+5
divide both sides by 5
y = 2/5x + 1
Thus, the y-intercept = 1
Now, please check the attached graph below.
The red line represents the equation 2x - 5y = -5
From the graph, it is clear that the red line has the y-intercept y = 1.
Now, considerng the equation 2
y = -3x + 1
comparing with the slope-intercept form of line equation
The y-intercept b = 1
Hence, the y-intercept of the line y = -3x + 1 is y = 1
The green line represents the equation y = -3x + 1
From the graph, it is clear that the green line has the y-intercept y = 1.
<u>Point of Intersection:</u>
It is clear from the graph:
As both lines meet or intersect at the point (0, 1).
Therefore, the point of intersection of both the lines is:
(x, y) = (0, 1)
As we know that the point of intersection of both the lines represents the solution to the system of equations.
Therefore, (0, 1) on the graph represents the solution to the system of equations.
The graph is attached below.
Answer:
Step-by-step explanation:
Given
See attachment for parallelogram
Required
Find variables x and y
Solving for x, we have:
---- Opposite sides of a parallelogram
------ Divide both sides by 5
Solving for y, we have:
---- Opposite sides of a parallelogram
------ Collect like terms
---- Divide both sides by 3
In order to be continuous everywhere, we only need to satisfy continuity at . For that to happen, we need to have
By the function's definition, . Compute the limits:
So we must have