$y=6x+16$ $-7x-y=36$ What is the solution $(x, y)$ to the given system of equations?

$(-\frac{20}{13},-\frac{80}{13})$

Math · Algebra

Systems of Linear Equations

Solve two-equation systems with substitution, elimination, or graphing.

What the SAT Tests

Systems of linear equations questions on the Digital SAT often involve solving for one variable or identifying when a system has no solution or infinitely many solutions.

Key Tips for Systems of Linear Equations

Pick elimination when coefficients line up cleanly, substitution when one variable is already isolated.
Parallel lines (same slope, different intercepts) = no solution.
Same line (proportional coefficients and constant) = infinite solutions.

How to recognize Systems of Linear Equations questions

Look for Algebra signals: equations, graphs, tables, variables, units, or words that describe a relationship.
Before solving, decide whether the answer should be a value, expression, coordinate, graph feature, or interpretation.
The official College Board skill label is Systems of two linear equations in two variables; match your practice misses to that label when reviewing.

Fast solving workflow

Translate the givens into an equation, graph, table, or labeled diagram before using answer choices.
Choose the fastest method: mental math for one-step work, paper algebra for clean symbolic steps, Desmos for intersections/tables/roots, and substitution for ordered answer choices.
Check the final answer against the question stem, especially units, signs, and whether it asks for x, y, a sum, a coefficient, or an interpretation.

Common traps

Solving for the wrong variable after doing the algebra correctly.
Dropping a negative sign when moving terms across the equals sign.
Reading slope or intercept without checking the units in the problem.

Sample Systems of Linear Equations Questions

These are real practice questions pulled from our Digital SAT bank. Try each one before reading the highlighted correct answer.

Question 1 · Easy
$4 x + y = 22$
$8 x - y = 2$
How many solutions does the given system of equations have?
- A. Infinitely many
- B. Zero
- C. Exactly two
- D. Exactly oneCorrect
Question 2 · Easy
Given the system of equations:
$x = 5$
$- 2 x + y = - 5$
What is the value of $x + y$ ?
- A. -20
- B. -10
- C. 10Correct
- D. 20
Question 3 · Easy
$y = 6 x + 16$
$- 7 x - y = 36$
What is the solution $(x, y)$ to the given system of equations?
- A. $(- 4, - 8)$ Correct
- B. $(- \frac{20}{13}, - \frac{80}{13})$
- C. $(4, 40)$
- D. $(20, 136)$

Practice Systems of Linear Equations Questions

Drill systems of linear equations questions in the Digital SAT Math question bank, or take a full-length practice module to see how this skill appears under test conditions.

Practice block	What to do	Move on when
Warmup	Solve 10 untimed systems of linear equations questions and write the rule used for each.	You can explain 8 of 10 without reading the explanation.
Timed drill	Solve 20 filtered bank questions at real module pace.	Accuracy is at least 80% and misses are not repeating.
Transfer	Take a mixed timed module and mark each Algebra miss.	The skill still holds up when mixed with other question types.

FAQs

What is Systems of Linear Equations on the Digital SAT?

Systems of linear equations questions on the Digital SAT often involve solving for one variable or identifying when a system has no solution or infinitely many solutions.

How hard are systems of linear equations questions?

Systems of Linear Equations questions appear at every difficulty level on the Digital SAT Math section. The hardest versions gate access to the top scaled scores in the hard Module 2.

How do I practice systems of linear equations?

Use the 1600.now question bank to filter for systems of linear equations questions, solve at least 20 in a row, and review every miss with the written explanation.

Related Math Skills

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