Equations in two variables and systems
Find the pairs that satisfy an equation in two variables, draw its graph, build a system from a story and find its solution.
- Ukraine: grade 7
- Russia: grade 9
Guide
Ukrainian Algebra 7 (§§ 24, 25, 29) teaches this: equations in two variables, the linear equation and its graph, and word problems with systems of equations.
A solution of an equation in two variables is an ordered pair (x; y) that makes it true. There are infinitely many. For example, the pair (2; 3) is a solution of x + y = 5.
The graph of ax + by = c is a line. To draw it, express y by x and find two points: from 2x + y = 4 you get y = −2x + 4.
Solve a word problem like this: name the unknowns x and y; write two equations from the story (a system); solve it; check the answer against the story; write the answer.
A solution of a system is a pair that satisfies both equations: on the graph, the crossing point of two lines.