Systems of Linear Equations Worksheets Grade 10

1. On a coordinate plane, Noah draws a trapezoid with vertices at A(7, 2), B(19, 2), C(15, 10), and D(9, 10). He then draws a diagonal from A to C. A second line passes through the midpoint of this diagonal and is perpendicular to side AB. Visualize this figure. Write the system of linear equations representing the two lines (the diagonal AC and the line through the midpoint perpendicular to AB), then find their intersection point.
2. A technology company is analyzing the optimal production mix for two new electronic devices. Device X requires 3 hours of assembly and 1 hour of quality testing, while Device Y requires 2 hours of assembly and 2 hours of quality testing. The factory has exactly 240 assembly hours and 160 quality testing hours available per week. If the company wants to use all available hours exactly, how many units of each device should they produce?
3. 2x + 3y = 19; 5x - 2y = 26; x = ?

…and 3 more problems

1. Sophia is managing the production of two types of custom furniture: a basic chair and an armchair. Each basic chair requires 7 units of wood and 4 units of upholstery fabric. Each armchair requires 9 units of wood and 8 units of upholstery fabric. The workshop has exactly 189 units of wood and 124 units of upholstery fabric available for the week. If Sophia wants to use all available materials exactly, how many of each type of chair should be produced?
2. Matiu is managing the inventory for a community garden that sells two types of compost: a standard mix and a premium mix. Each bag of standard mix requires 5 kilograms of green waste and 3 kilograms of brown waste. Each bag of premium mix requires 7 kilograms of green waste and 5 kilograms of brown waste. The garden has exactly 185 kilograms of green waste and 115 kilograms of brown waste available. Matiu wants to use all the green waste and all the brown waste exactly, with no leftovers. How many bags of each type of compost should he produce?
3. Emma is organizing a school fundraiser selling two types of gift baskets: a standard basket and a deluxe basket. Each standard basket requires 3 hours of preparation and 1 hour of packaging, while each deluxe basket requires 5 hours of preparation and 3 hours of packaging. The volunteer team has exactly 51 hours available for preparation and 25 hours available for packaging each week. If Emma wants to use all available hours exactly, how many of each type of gift basket should they produce each week?

…and 2 more problems

1. Mere is designing a geometric pattern on a coordinate grid. She draws a triangle with vertices at A(10, 20), B(30, 50), and C(50, 10). She then draws the three medians of this triangle (lines from each vertex to the midpoint of the opposite side). Visualize this triangle and its medians on the grid. Write the system of linear equations representing two of these medians (the median from A to side BC and the median from B to side AC), then find the coordinates of their intersection point (the centroid).
2. On a coordinate plane, Emma draws a parallelogram with vertices at A(1, 1), B(7, 1), C(9, 5), and D(3, 5). She then draws a diagonal from A to C. A second line passes through the midpoint of this diagonal and is parallel to side AB. Visualize this figure. Write the system of linear equations representing the two lines (the diagonal AC and the line through the midpoint parallel to AB), then find their intersection point.
3. Solve: 7x + 3y = 31; 5x - 3y = 11; x = ?

…and 3 more problems