8. On a graph paper draw two straight lines which represent the equations 2x-y=3 and 3x+2y=1. Also, find the point of intersection of the two lines on the graph paper.
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To graph the equations 2x - y = 3 and 3x + 2y = 1, we need to find two points on each line and then connect them to draw the lines.
Let's find points for each equation:
For 2x - y = 3: Let x = 0: 2(0) - y = 3 y = -3 So, one point is (0, -3).
Let y = 0: 2x - 0 = 3 x = 3/2 So, another point is (3/2, 0).
For 3x + 2y = 1: Let x = 0: 3(0) + 2y = 1 y = 1/2 So, one point is (0, 1/2).
Let y = 0: 3x + 2(0) = 1 x = 1/3 So, another point is (1/3, 0).
Now, plot these points on the graph paper and draw the lines passing through them. The two lines should intersect at a certain point. The point of intersection will be the solution to the system of equations.
Upon plotting and drawing the lines, you will find that the point of intersection is approximately (1, -1).
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Step-by-step explanation:
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Let's find points for each equation:
For 2x - y = 3:
Let x = 0:
2(0) - y = 3
y = -3
So, one point is (0, -3).
Let y = 0:
2x - 0 = 3
x = 3/2
So, another point is (3/2, 0).
For 3x + 2y = 1:
Let x = 0:
3(0) + 2y = 1
y = 1/2
So, one point is (0, 1/2).
Let y = 0:
3x + 2(0) = 1
x = 1/3
So, another point is (1/3, 0).
Now, plot these points on the graph paper and draw the lines passing through them. The two lines should intersect at a certain point. The point of intersection will be the solution to the system of equations.
Upon plotting and drawing the lines, you will find that the point of intersection is approximately (1, -1).