Solve Systems Exactly Worksheets Grade 9

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (0,8). A circle is circumscribed around this triangle, passing through all three vertices. Visualize the triangle inside the circle with the circle's circumference touching each vertex. What is the area of the circumscribed circle?
2. Matiu is designing a rectangular garden that is surrounded by a uniform gravel path. The garden itself has a length that is 4 meters more than its width. The total area of the garden and the path together is 140 square meters. The path is 2 meters wide on all sides. Find the exact dimensions (length and width) of the garden.
3. On a coordinate plane, Liam draws a parabola that opens upward with vertex at (3, 1) and a line that passes through the points (1, 5) and (5, 5). The parabola and the line intersect at two points. Visualize this graph. What are the exact coordinates of the two intersection points?

…and 4 more problems

1. Solve the system: 3x + 2y = 7 and 5x - 4y = 2
2. Solve the system: y = x² - 9x + 20 and y = 2x - 10.
3. Solve the system: 3x - 2y = 7 and 5x + 4y = 8

…and 5 more problems

1. On a coordinate plane, Aroha draws a parabola with equation y = x^2 - 7 and a line with equation y = 2x + 1. Visualize these two graphs intersecting. What are the exact coordinates of their intersection points?
2. Solve the system: y = x² - 6x + 11 and y = 2x - 1.
3. Solve the system: 3x² - 2x + 5 = y and 2x² + 4x - 1 = y

…and 6 more problems