A pair of linear equations drawn as two lines. When the lines cross, run parallel or coincide, and how the coefficients tell you which without drawing.
3 lessons, about 1 h 15 min3 simulations10 problems6 practice questionsPython in every lesson
Created by StemPy LabA linear equation in two variables has many solutions, and its graph is a straight line. A pair of such equations states two conditions at once. A solution of the pair is a point that lies on both lines. Draw each line from a table of values, read the common point, and check it in both equations.
Two straight lines can cross at one point, run side by side, or lie on top of each other. These three cases give exactly one solution, no solution and infinitely many solutions. A pair with at least one solution is consistent, a pair with none is inconsistent, and the equations of a pair whose lines coincide are dependent.
For a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, compare the ratios a1/a2, b1/b2 and c1/c2. Different first two ratios mean crossing lines. Equal first two ratios with a different third mean parallel lines. Three equal ratios mean one line. Use the test to find a missing number k, and read the answer from the graph of a real situation.
Log in to join the discussion.
Loading…