Solve Systems Exactly Worksheets Grade 9

1. Solve the system: 3x - 2y = 7 and 2x + 5y = -4
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. A chemistry lab needs to mix two solutions with different concentrations of hydrochloric acid. Solution A contains 15% acid and Solution B contains 40% acid. The lab technician wants to create 500 milliliters of a solution that contains exactly 28% acid. Write and solve a system of equations to determine how many milliliters of each solution should be mixed.

…and 4 more problems

1. Solve the system: 3x² - 2x + 5 = 2x² + 3x - 1 and 4x - y = 7
2. On a coordinate plane, Noah draws a parabola and a line. The parabola is represented by the equation y = x² - 6x + 11. The line passes through the points (1, 6) and (6, 16). Visualize the graph where the line intersects the parabola at two points. Find the exact coordinates of both intersection points.
3. A chemistry lab needs to mix two solutions with different concentrations of acid. Solution A contains 25% acid and Solution B contains 40% acid. The lab technician wants to create 200 milliliters of a mixture that contains 32% acid. Write and solve a system of equations to determine exactly how many milliliters of each solution should be used.

…and 4 more problems

1. x² + y² = 73, y = 3x + 1. Solve system.
2. 2x + 3y = 12 and 3x - 2y = 5
3. Liam is designing a rectangular garden with a perimeter of 40 meters. He wants the length to be 4 meters more than twice the width. Write a system of equations to represent this situation and solve it exactly to find the dimensions of Liam's garden.

…and 5 more problems