Download CHECK FOR UNDERSTANDING: Solve equations by inspection

CHECK FOR UNDERSTANDING: Solve equations by inspection
Scroll to the second page to view the answer key and explanations.
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Answer Key and Explanations
1) Infinitely many solutions. The first equation is 𝑦 = 2𝑥 − 3. If you add “2x” to both sides of the second equation,
you also get 𝑦 = 2𝑥 − 3. These two equations match perfectly, so they are overlapping or simultaneous
equations.
2) No solution. The first equation (if I subtract 3x from both sides to isolate y) is 𝑦 = −3𝑥 + 4. The second equation
(if I add 7 to both sides to isolate y) is 𝑦 = −3𝑥 + 7. These two equations have the same slope but different yintercepts. They are parallel lines and will never intersect, so they have no solution.
3) No solution. The first equation is 𝑦 = −4𝑥 + 1. The second equation (if I isolate y) is 𝑦 = −4𝑥 − 6. [Tip: Ask a
friend or teacher for help if you are not sure how I got this equation]. The two equations have the same slope
but different y-intercepts. They are parallel lines and will never intersect, so they have no solution.
4) Infinitely many solutions. The second equation is 𝑥 = 𝑦 + 3. The first equation (if I isolate x by adding “x” to
both sides) is also 𝑥 = 𝑦 + 3. These two equations match perfectly, so they are overlapping or simultaneous
equations.
5) Infinitely many solutions. Look at the two equations and notice that each part of the first equation is exactly 3
times greater than the second equation. When this is the case, the two equations are actually the exact same
equation in disguise! These two equations match perfectly, so they are overlapping or simultaneous equations.
6) Infinitely many solutions. The first equation is 𝑦 = 3𝑥 − 2. If you isolate y in the second equation by adding “3x”
to both sides, then the second equation is also 𝑦 = 3𝑥 − 2. These two equations match perfectly, so they are
overlapping or simultaneous equations.
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7) One distinct solution. The first equation is 𝑦 = 2 𝑥 − 1. If you divide both sides of the second equation by 3 to
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isolate y, you get 𝑦 = 3 𝑥 + 3. Since the two equations have different slopes, they will inevitably intersect each
other at one point.
8) No solution. This problem is similar to problem 5 except with one major difference. In this case, the first
equation is exactly 3 times bigger than the second equation except for the number at the end (the “constant”).
Think of that number at the end as being part of the y-intercept. If these numbers do not follow the same
pattern as the rest of the equations, then it tells us that the slope will be the same but the y-intercepts are