Grade 10 — Mathematics 10C › C10U08 Systems of Linear Equations

Grade 10 › C10U08 Systems of Linear Equations › L1
GRADE 10 · ALBERTAOUTCOME RF9

L1 · Systems and Their Graphical Solutions

Learning goal

“I can explain what a system of linear equations is, read its solution from a graph described by the two lines, state what the point of intersection means, and verify the solution by substituting it into BOTH original equations.”

System of linear equations — two (or more) linear equations considered together, sharing the same two variables.
Solution of a system — an ordered pair (x, y) that makes BOTH equations true at the same time.
Point of intersection — the point where the two graphs cross; its coordinates are the solution of the system.
Verify — to substitute a candidate solution into the original equations and check that both sides balance in each one.
Worked example

A graph shows two lines: Line 1: y = 2x + 1, drawn through (0, 1) and (3, 7). Line 2: y = -x + 7, drawn through (0, 7) and (7, 0). The lines cross at exactly one point: (2, 5). Step 1: Read the crossing point off the graph: x = 2, y = 5. Step 2: Verify in Line 1's equation: 2(2) + 1 = 5 ✓ - (2, 5) really is on Line 1. Step 3: Verify in Line 2's equation: -(2) + 7 = 5 ✓ - (2, 5) really is on Line 2. Say it plainly: a point on one line answers one equation. The crossing point is special because it is the ONE point that answers both at once. Reading it off the graph is the claim; substituting into both equations is the proof.

Check yourself — explain it

Why must the solution of a system be checked in BOTH equations, not just one?

Paired problem — example still visible

A graph shows y = x + 2 (through (0, 2) and (4, 6)) and y = 3x - 4 (through (0, -4) and (2, 2)) crossing at one point. State the solution and verify it. -> (3, 5); check: 3 + 2 = 5 ✓ and 3(3) - 4 = 5 ✓

Faded completion — last step is yours

"The lines y = 4x - 3 and y = x + 3 cross at (2, ___). The missing coordinate comes from either equation: 4(2) - 3 = ___" -> 5; 5

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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