To review the graphs of this system of two linear equations, let's start by graphing each equation individually and then analyze where they intersect.
The first equation, x - 5y = 7, can be rewritten in the slope-intercept form as y = (1/5)x - 7/5. We can identify that the slope is 1/5 and the y-intercept is -7/5.
Let's plot some points to graph this equation:
For x = 0, y = -7/5:
(0, -7/5)
For x = 5, y = -6/5:
(5, -6/5)
Joining these two points and extending the line:
Graph of equation 1:
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(-2,-2)
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| \
| \
| \
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*------*
(0,-7/5)
Now let's move on to the second equation, 3x - 2y = -4, which can be rearranged to y = (3/2)x + 2. Here, the slope is 3/2 and the y-intercept is 2.
Let's plot some points to graph this equation:
For x = 0, y = 2:
(0, 2)
For x = 2, y = 5:
(2, 5)
Joining these two points and extending the line:
Graph of equation 2:
(0,2)*-----------------------
| /
| /
| /
| /
| /
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-7.5 | /
| /
| /
*---------* (2,5)
-4
Now, let's analyze the intersection point where these two lines intersect:
Intersection Point:
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(-2,-2)
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| \
| \
| \
| \
| \
*------*
(0,-7/5)
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*---------* (2,5)
-4
From the graph, the intersection point occurs at approximately (2, 5).
Therefore, the solution to the system of equations is (2, 5).
This visual representation of the system of equations helps us understand where the two lines intersect and provides a visual confirmation of the solution.
review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 2y = -4
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