Simultaneous Equations
Simultaneous equations are two (or more) equations that share the same unknowns. Solving them together finds the values that satisfy all equations at once.
What You Need to Know
Key Concept Diagram
Substitution method: solve one equation for one variable, substitute into the other
Elimination method: add or subtract equations to remove one variable
The solution is the point (x, y) where two lines intersect on a graph
If lines are parallel, there is no solution; if they are the same line, infinitely many solutions
Key Vocabulary
Simultaneous equations
Two or more equations with the same variables that must be solved together
Substitution
Replacing a variable with an equivalent expression from another equation
Elimination
Adding or subtracting equations to remove one variable
Solution
The values of the variables that satisfy all equations simultaneously
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Solve: x + y = 10 and x - y = 4. What is x?
Question 2
Using substitution for y = 2x and x + y = 9, find x.
Question 3
Two lines have equations y = 3x + 1 and y = 3x - 4. How many solutions do they share?
Key Concepts Summary
- ●Substitution method: solve one equation for one variable, substitute into the other
- ●Elimination method: add or subtract equations to remove one variable
- ●The solution is the point (x, y) where two lines intersect on a graph
- ●If lines are parallel, there is no solution; if they are the same line, infinitely many solutions