How to explain it
At this standard, students solve systems of two linear equations using substitution: isolate, substitute, solve, and back-substitute to find the ordered-pair solution.
The anchor students hold onto: Step 1: Solve one equation for one variable. Step 2: Substitute. Step 3: Solve. Step 4: Back-substitute to find the other variable. Step 1: Line up equations in standard form. Step 2: Multiply to match a pair of coefficients. Step 3: Add or subtract to eliminate. Step 4: Solve, then back-substitute.
Students use this for 8.EE.C.8c real-world systems and for #83 Systems by Elimination — a second algebraic method that reaches the same intersection a different way.
Worked examples
Example 1
Already Isolated
y = 2x − 1 ; 3x + y = 9
Step 1Substitute y = 2x − 1 into eq 2.
Step 23x + (2x − 1) = 9 → 5x − 1 = 9
Step 35x = 10 → x = 2
Step 4Back-sub: y = 2(2) − 1 = 3
Answer(2, 3) → Q1
Example 2
One-Step Isolate
x + y = 2 ; 3x − y = −6
Step 1Solve eq 1 for y: y = 2 − x.
Step 2Sub into eq 2: 3x − (2 − x) = −6
Step 34x − 2 = −6 → 4x = −4 → x = −1
Step 4Back-sub: y = 2 − (−1) = 3
Answer(−1, 3) → Q2
Example 3
Strategic Choice
3x + y = −5 ; 2x − 3y = 4
Step 1Isolate y in eq 1: y = −5 − 3x
Step 2Sub into eq 2: 2x − 3(−5 − 3x) = 4
Step 311x = −11 → x = −1
Step 4Back-sub: y = −5 − 3(−1) = −2
Answer(−1, −2) → Q3
Common mistakes
What students write
Substituting back into the SAME equation, which gives a useless true statement like 9 = 9.
The fix
Always substitute the expression into the OTHER equation.
What students write
Dropping parentheses around a multi-term expression, so the sign of the second term is wrong.
The fix
Wrap the substituted expression in parentheses, then distribute.
What students write
Multiplying only the variable terms when scaling — for example, writing 2(x + 3y = 5) as 2x + 3y = 10 instead of 2x + 6y = 10.
The fix
Multiply EVERY term including the constant on the right side by the same number.
What students write
Choosing the wrong operation — adding when coefficients are equal (same sign), or subtracting when signs are opposite.
The fix
Equal signs → SUBTRACT. Opposite signs → ADD. Ask: which operation makes one variable cancel?
Teacher tip
Head off the two predictable errors before they happen. First: Always substitute the expression into the OTHER equation. Second: Wrap the substituted expression in parentheses, then distribute.