How does y = 2x + 1 help you solve x + y = 10?
Two equations with two unknowns feel harder than one. Substitution turns the pair into a single equation with one letter.
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1 lesson for “Systems of equations: substitution”
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How does subtracting the equations remove a variable?
When both equations share a term like 2y, that term becomes your exit: subtract the equations and it disappears.
Try this lessonWhat is the opposite of adding 7?
Owen solved x + 7 = 12 by computing 12 + 7 = 19. He added again instead of undoing the addition.
Try this lessonWhere did the negative sign go?
A negative sign belongs to the number next to it. Keeping that number together can prevent an almost-correct equation from turning into the wrong answer.
Try this lessonWhich move comes first?
Isla solved 3x + 4 = 19 by writing 3x = 23, giving x = 23/3. She never removed the +4 before dividing.
Try this lessonWhy can't I just move the x?
Milo solved 3x + 2 = x + 10 by adding x to both sides: 4x = 12, so x = 3. Substitution showed 11 does not equal 13.
Try this lessonWhy can't you balance by changing H2O to H4O2?
Water is H2O, not H4O2. Learn how coefficients balance an equation without inventing new molecules.
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