To review the graphs of the system of equations x−5y=7 and 3x−2y=−4, we can rewrite both equations in slope-intercept form (y = mx + b).
1. For the first equation, we have x − 5y = 7. To rewrite it in slope-intercept form, we isolate y:
-5y = -x + 7
y = (1/5)x - 7/5
2. For the second equation, we have 3x − 2y = -4. Isolating y, we get:
-2y = -3x - 4
y = (3/2)x + 2
Now, let's plot the graphs of both equations:
Graph 1:
The equation y = (1/5)x - 7/5 represents a line with a slope of 1/5 and a y-intercept of -7/5. When x = 0, y = -7/5, and when y = 0, x = 7. Therefore, we have the points (0, -7/5) and (7, 0). Drawing a line passing through these points, we get:
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Graph 2:
For the equation y = (3/2)x + 2, the slope is 3/2, and the y-intercept is 2. When x = 0, y = 2, and when y = 0, x = -4/3. So, we have the points (0, 2) and (-4/3, 0). Drawing the line passing through these points, we get:
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The solution to the system of equations can be found by identifying the point of intersection on the graph. Looking at the graphs, we can see that the lines intersect at the point (-3, -1).
Therefore, the solution to both equations is x = -3 and y = -1.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4 . Find the solution to both equations.
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1 answer