{"id":10979,"date":"2022-06-10T19:41:11","date_gmt":"2022-06-10T14:11:11","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10979"},"modified":"2022-06-11T04:50:17","modified_gmt":"2022-06-10T23:20:17","slug":"draw-the-graph-of-the-equation-x-y-1-0-and-3x-2y-12-0-determine-the-coordinates-of-the-vertices-of-the-triangle-formed-by-these-lines-and-the-x-axis-and-shade-the-triangular-region","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/draw-the-graph-of-the-equation-x-y-1-0-and-3x-2y-12-0-determine-the-coordinates-of-the-vertices-of-the-triangle-formed-by-these-lines-and-the-x-axis-and-shade-the-triangular-region\/","title":{"rendered":"Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region."},"content":{"rendered":"\n
Solution :<\/h2>\n\n\n\n
Given Pair of linear equations are :<\/p>\n\n\n\n
x – y + 1 = 0 ……(i)<\/p>\n\n\n\n
and 3x + 2y – 12 = 0 …….(ii)<\/p>\n\n\n\n
first we find points for equation (i),<\/p>\n\n\n\n
x<\/td>
0<\/td>
4<\/td><\/tr>
y = x + 1<\/td>
1<\/td>
5<\/td><\/tr>
Points<\/td>
A<\/td>
B<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
second we find points for equation (ii),<\/p>\n\n\n\n
x<\/td>
0<\/td>
4<\/td><\/tr>
y = \\(12 – 3x\\over 2\\)<\/td>
6<\/td>
0<\/td><\/tr>
Points<\/td>
C<\/td>
E<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Now, plot the points A(0,1), B(4, 5) and join them to get AB.<\/p>\n\n\n\n
Similarly, plot the points in second table i.e. points C, E and join them to form a line CE.<\/p>\n\n\n\n<\/figure>\n\n\n\n
Clearly, the two lines AB and CE intersect each other at the point D(2, 3).<\/p>\n\n\n\n
Hence, the solution of the given pair of linear equations is x = 2 and y = 3.<\/p>\n\n\n\n
Hence, the triangle formed is having vertices with the coordinates : D(2, 3), E(4, 0), F(-1, 0).<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"
Solution : Given Pair of linear equations are : x – y + 1 = 0 ……(i) and 3x + 2y – 12 = 0 …….(ii) first we find points for equation (i), x 0 4 y = x + 1 1 5 Points A B second we find points for equation (ii), x 0 …<\/p>\n
![\"\"](\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-2-7.jpeg?fit=278%2C300&ssl=1\")
<\/figure>\n\n\n\n