Systems of Equations — Digital SAT SAT Math revision notes
A 3-page visual revision sheet for Systems of Equations, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Systems of Equations in one look
two lines, one question: where do they meet, and do they meet at all
A system, and what solving it means
- the pair, in standard form
a_1x + b_1y = c_1 - and
a_2x + b_2y = c_2 - a solution is an ordered pair
(x, y) satisfying BOTH - graphically, the solution is
the point where the lines cross
Q. Solve 2x + 3y = 16 and 5x - 3y = 19, then give the value of x + y.
- the y terms are already opposites, so add the two equations: 7x = 35
- x = 5
- put x = 5 back into the first: 10 + 3y = 16, so 3y = 6
- y = 2, and the question wants x + y
Answer: (x, y) = (5, 2), so x + y = 7
Q. Solve y = 4x - 7 and 3x + 2y = 8.
- one equation is already solved for y, so substitute it into the other
- 3x + 2(4x - 7) = 8
- 3x + 8x - 14 = 8, so 11x = 22
- x = 2, then y = 4(2) - 7
Answer: (x, y) = (2, 1)
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Systems of Equations sheet covers
- A system, and what solving it means
- the pair, in standard form
- and
- a solution is an ordered pair
- graphically, the solution is
- Three pictures, three answers
- Traps that cost points
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Systems of Equations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.
More SAT Math revision notes
- Area and Volume
- Circles
- Equivalent Expressions and Polynomials
- Evaluating Statistical Claims
- Inference and Margin of Error
- Linear Equations
- Linear Functions
- Linear Inequalities
- Lines, Angles, Triangles
- Nonlinear Equations in One Variable
- Nonlinear Functions
- Nonlinear Systems
- One-variable Data
- Percentages
- Probability and Conditional Probability
- Ratios, Rates and Proportions
- Triangles and Trigonometry
- Two-variable Data
- Units, Rates and Conversions