
system of equations substitution
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a system of equations?
Back
A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.
2.
FLASHCARD QUESTION
Front
What does substitution mean in the context of solving equations?
Back
Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.
3.
FLASHCARD QUESTION
Front
How do you solve the system: y = 8x + 1 and y = 6x + 3?
Back
Set 8x + 1 = 6x + 3. Solve for x to find x = 1, then substitute back to find y = 9. The solution is (1, 9).
4.
FLASHCARD QUESTION
Front
What is the first step in using substitution to solve a system of equations?
Back
The first step is to solve one of the equations for one variable in terms of the other variable.
5.
FLASHCARD QUESTION
Front
How do you solve the system: y = 3 - x and 3y + x = 5?
Back
Substitute y = 3 - x into 3y + x = 5. This gives 3(3 - x) + x = 5. Solve to find x = 2, then y = 1. The solution is (2, 1).
6.
FLASHCARD QUESTION
Front
What is the solution to the system: x = 6 and y = 2x - 3?
Back
Substituting x = 6 into y = 2(6) - 3 gives y = 9. The solution is (6, 9).
7.
FLASHCARD QUESTION
Front
How do you solve the system: 2y + x = -15 and x = 3y?
Back
Substitute x = 3y into 2y + 3y = -15. This gives 5y = -15, so y = -3. Then, x = 3(-3) = -9. The solution is (-9, -3).
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