{"id":11237,"date":"2022-06-29T15:13:38","date_gmt":"2022-06-29T09:43:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11237"},"modified":"2022-06-29T15:14:49","modified_gmt":"2022-06-29T09:44:49","slug":"draw-the-graphs-of-the-equation-5x-y-5-and-3x-y-3-determine-the-coordinates-of-the-vertices-of-the-triangle-formed-by-these-lines-and-the-y-axis","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/draw-the-graphs-of-the-equation-5x-y-5-and-3x-y-3-determine-the-coordinates-of-the-vertices-of-the-triangle-formed-by-these-lines-and-the-y-axis\/","title":{"rendered":"Draw the graphs of the equation 5x – y = 5 and 3x – y = 3. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis."},"content":{"rendered":"\n
Solution : <\/h2>\n\n\n\n
The given linear equations are<\/p>\n\n\n\n
5x – y = 5 ………(1)<\/p>\n\n\n\n
3x – y = 3 ………(2)<\/p>\n\n\n\n
From equation (1), y = 5x – 5<\/p>\n\n\n\n
When x = 1, y = 5 – 5 = 0<\/p>\n\n\n\n
When x = 2, y = 10 – 5 = 5<\/p>\n\n\n\n
x<\/td>
1<\/td>
2<\/td><\/tr>
y<\/td>
0<\/td>
5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
From equation (2), y = 3x – 3<\/p>\n\n\n\n
When x = 0, y = -3<\/p>\n\n\n\n
When x = 2, y = 3<\/p>\n\n\n\n
x<\/td>
0<\/td>
2<\/td><\/tr>
y<\/td>
-3<\/td>
3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Now, plot the above points on the graph, we get two lines.<\/p>\n\n\n\n
We see that the line meets y-axis, the value of x is 0. In the equation 5x – y = 5, for x = 0, we get y = – 5.<\/p>\n\n\n\n
Thus, the line 5x – y = 3 meets the y-axis at (0, -5).<\/p>\n\n\n\n
and the line 3x – y = 3 meets the y-axis at (0, -3).<\/p>\n\n\n\n
Thus, the coordinates of \\(\\triangle\\) ACE formed by these two lines and the y-axis A(1, 0), C(0, – 3) and E(0, -5)<\/strong>.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Solution : The given linear equations are 5x – y = 5 ………(1) 3x – y = 3 ………(2) From equation (1), y = 5x – 5 When x = 1, y = 5 – 5 = 0 When x = 2, y = 10 – …<\/p>\n
![\"\"](\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-7-6.jpeg?fit=206%2C300&ssl=1\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"