System Solvers Slides 8th Grade Math
System Solvers
Cracking Systems of Equations
X = ?
Y = ?
The Goal
A System is just two equations working together.
The Solution is the (x, y) point that makes BOTH equations true.
Tool 1: Substitution
Best for:
When one equation is already solved for x or y.
Example:
y = 2x
x + y = 6
The Process:
1 Circle what "y" equals.
2 Plug it into the other equation.
3 Solve for the first variable.
Training Case: Substitution
The System:
y = 3x
x + y = 20
Steps:
1. Replace y with (3x)
2. New Equation: x + 3x = 20
3. Solve: x = 5
Wait! If x = 5, what is y? (y = 3 × 5)
Tool 2: Elimination
Best for:
Equations are stacked and variables line up.
Example:
x + y = 10
x - y = 4
The Power Move:
1 Check for "opposites" (y and -y).
2 Add the equations together.
3 The opposites cancel out!
Training Case: Elimination
The System:
3x + y = 10
x - y = 6
4x = 16
Watch closely!
1. The +y and -y are opposites.
2. Add them: 3x + x = 4x
3. 10 + 6 = 16
4. Final answer for x: x = 4
Ready to Solve?
Grab your System Solvers Packet. Complete the training cases, then show your skills on the independent work!
10 Minutes Guided
10 Minutes Solo
System Solvers Packet System Solvers
Review Packet: Substitution & Elimination
Name:
Date:
Method 1: Substitution
Training 01
y = 4x
x + y = 15
Workspace (Plug in and solve)
Training 02
2x + y = 12
y = 2x
Workspace
Method 2: Elimination
Training 03
x + y = 12
x - y = 2
Add Columns
Workspace
Independent Work
Prob 01 y = 5x ; x + y = 12
Substitution
Work Area
Answer:
( x = ___ , y = ___ )
Prob 02 2x + y = 10 ; 2x - y = 2
Elimination
Work Area
Answer:
( x = ___ , y = ___ )
Prob 03 y = x + 2 ; x + y = 4
Method Choice
Work Area
Answer:
( x = ___ , y = ___ )
Solution Sum Check
Add your three x-values. The sum should be 6.
=
?
System Solvers Answer Key Answer Key
System Solvers Packet • Teacher Resource
Check Sum
6
Guided Training Solutions
Training 01: y = 4x ; x + y = 15
x + (4x) = 15 → 5x = 15 → x = 3
y = 4(3) → y = 12
Solution: (3, 12)
Training 02: 2x + y = 12 ; y = 2x
2x + (2x) = 12 → 4x = 12 → x = 3
y = 2(3) → y = 6
Solution: (3, 6)
Training 03: x + y = 12 ; x - y = 2
2x = 14 → x = 7
7 + y = 12 → y = 5
Solution: (7, 5)
Independent Work Solutions
#01
y = 5x; x + y = 12
x + 5x = 12 → 6x = 12 → x = 2 ; y = 5(2) = 10
Answer: (2, 10)
#02
2x + y = 10; 2x - y = 2
4x = 12 → x = 3 ; 2(3) + y = 10 → 6 + y = 10 → y = 4
Answer: (3, 4)
#03
y = x + 2; x + y = 4
x + (x + 2) = 4 → 2x = 2 → x = 1 ; y = 1 + 2 = 3
Answer: (1, 3)
MASTER SUM VERIFICATION
Problem 01 (x=2) + Problem 02 (x=3) + Problem 03 (x=1)
6
