➕ Algebra 1 · Systems of Equations
Solving Systems by Elimination flashcards
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All 16 flashcards at a glance
Card 1
What is the goal of the elimination method?
Add or subtract the two equations so that one variable cancels, leaving an equation with only one variable.
Card 2
When do you add the two equations to eliminate a variable?
When that variable's coefficients are opposites (they add to 0), such as 6y and −6y.
Card 3
When do you subtract one equation from the other to eliminate a variable?
When that variable has the same coefficient in both equations, such as 4x and 4x. Subtract every term of the second equation, so every sign in it flips.
Card 4
Subtract the second equation from the first: x + 2y = 9 and x − 4y = 3. What do you get?
6y = 6. The minus reaches both terms: 2y − (−4y) = 6y, and 9 − 3 = 6. So y = 1, and then x = 7.
Card 5
Solve x + 2y = −1 and 3x − 2y = 21.
(5, −3). Add: 4x = 20, so x = 5. Then 5 + 2y = −1 gives y = −3. Check the second equation: 15 + 6 = 21.
Card 6
To eliminate x from x + 3y = 10 and 3x + y = 6, what do you multiply the first equation by, and what do you get?
Multiply every term by 3: 3x + 9y = 30 (the 10 becomes 30). Subtract 3x + y = 6 to get 8y = 24, so y = 3 and x = 1.
Card 7
You multiply 7x − 2y = 5 by 4. What is the new equation?
28x − 8y = 20. Every term is multiplied, including the constant.
Card 8
Elimination leaves 0 = 9. What does that mean?
No solution. The leftover is false for every x and y, so no pair makes both equations true (the lines are parallel).
Card 9
Elimination leaves 0 = 0. Does that mean x = 0 and y = 0?
No. A true leftover means the two equations describe the same line, so there are infinitely many solutions. The point (0, 0) may not even be on that line.
Card 10
After elimination gives x = 4, why is x = 4 not the solution of the system?
The solution of a system is an ordered pair (x, y). You still need to back-substitute to find y.
Card 11
Why check a solution in both original equations?
The equation you used to find the second value is satisfied by the way you found it (barring an arithmetic slip), so the other equation tests your elimination step. Use the originals, not rewritten versions, to catch slips made while rewriting.
Card 12
Why is it allowed to add two equations?
If both are true for the same x and y, the second equation says two expressions are equal. Adding equal amounts to both sides of the first equation keeps it true: if A = B and C = D, then A + C = B + D.
Card 13
Why can you multiply an equation by a number, and which number is not allowed?
Multiplying both sides by the same number keeps the equation balanced. Zero is not allowed, because it turns the equation into 0 = 0 and loses all the information.
Card 14
In this lesson's LAMBS memory trick, what do the letters stand for?
Line up in standard form, Adjust (multiply every term) so a variable matches, Merge (add or subtract) and solve, Back-substitute, Show it works in both original equations.
Card 15
Solve x + 4y = 5 and 3x − 4y = 7.
(3, 1/2). Add: 4x = 12, so x = 3. Then 3 + 4y = 5 gives 4y = 2, so y = 1/2. Check the second equation: 9 − 2 = 7. A solution can have a fraction in it.
Card 16
When might you choose substitution instead of elimination?
When one variable is already alone, like y = 4x − 9. Elimination still works after you rewrite that equation in standard form, so it is a choice, not a rule.