SAT Math: Linear Equations and Systems Flashcards

Question 1

Define Linear Equation in One Variable.

Accepted Answer

An equation that can be written as ax + b = c, where a is not zero and x appears only to the first power, so it has exactly one solution.

Question 2

Define Linear Equation in Two Variables.

Accepted Answer

An equation relating x and y, with both to the first power and no product xy, whose solutions are infinitely many ordered pairs that together form a straight line.

Question 3

Define Slope Formula.

Accepted Answer

The slope between two points (x₁, y₁) and (x₂, y₂) is (y₂ − y₁) ÷ (x₂ − x₁): the change in y divided by the change in x.

Question 4

Define Slope in Context.

Accepted Answer

In a real-world linear model, the slope is the amount the output changes for each one-unit increase in the input, stated with both units.

Question 5

Define Slope-Intercept Form.

Accepted Answer

The arrangement y = mx + b, which shows the steepness of a line and where it crosses the vertical axis without any further rearranging.

Question 6

Define Point-Slope Form.

Accepted Answer

The equation y − y₁ = m(x − x₁), which writes a line directly from its slope m and any one known point (x₁, y₁) on it.

Question 7

Define Slope From Standard Form.

Accepted Answer

For a line written as Ax + By = C with B not zero, the slope is −A ÷ B and the y-intercept is C ÷ B, so no rearranging is needed.

Question 8

What is X-Intercept?

Accepted Answer

The point where a graph crosses the horizontal axis, found by setting y equal to 0 and solving for x.

Question 9

Define Horizontal Line.

Accepted Answer

A line with slope 0, written y = k, where every point has the same y-value no matter what x is.

Question 10

Define Vertical Line.

Accepted Answer

A line written x = k whose slope is undefined, because every pair of points on it has a change in x of zero.

Question 11

Define Negative Reciprocal.

Accepted Answer

The number formed by flipping a fraction and changing its sign. A line at a right angle to another has a slope equal to the other's negative reciprocal.

Question 12

Define Equivalent Equations.

Accepted Answer

Equations that have exactly the same solution set, produced by doing the same allowed operation to both sides of an equation.

Question 13

Define Inverse Operations.

Accepted Answer

Pairs of operations that undo each other, such as addition and subtraction or multiplication and division, used in reverse order to isolate a variable.

Question 14

Define Distributive Property.

Accepted Answer

The rule a(b + c) = ab + ac, which removes brackets by multiplying the outside factor by every term inside them.

Question 15

Define Like Terms.

Accepted Answer

Terms with the same variable raised to the same power, which can be combined by adding or subtracting their coefficients.

Question 16

Define Literal Equation.

Accepted Answer

An equation containing several letters, such as a formula, that you rearrange to express one chosen variable in terms of the others.

Question 17

Define No-Solution Linear Equation.

Accepted Answer

An equation ax + b = cx + d has no solution when the x-coefficients match (a = c) but the constants differ (b ≠ d), leaving a false statement.

Question 18

Define Identity (Infinitely Many Solutions).

Accepted Answer

An equation whose two sides simplify to the same expression, so every value of the variable makes it true; ax + b = cx + d with a = c and b = d.

Question 19

Define System of Linear Equations.

Accepted Answer

Two or more linear equations that share the same variables and must all be true at once; its solution is any point satisfying every equation.

Question 20

Define Checking a Solution.

Accepted Answer

Substituting a proposed ordered pair into every equation of a system to confirm both sides are equal each time, a fast way to eliminate answer choices.

Question 21

Define Substitution Method.

Accepted Answer

Solving a system by rewriting one equation as a single variable expressed in the other, then replacing that variable in the second equation.

Question 22

Define Elimination Method.

Accepted Answer

Solving a system by scaling one or both equations so a variable's coefficients are opposites, then adding the equations to cancel that variable.

Question 23

Define No-Solution System Condition.

Accepted Answer

Two equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ have no solution when a₁/a₂ = b₁/b₂ but that ratio differs from c₁/c₂.

Question 24

Define Infinite-Solutions System Condition.

Accepted Answer

A system of two linear equations has infinitely many solutions when one equation is a constant multiple of the other, so a₁/a₂ = b₁/b₂ = c₁/c₂.

Question 25

Define One-Solution System Condition.

Accepted Answer

A system of two linear equations has exactly one solution whenever the lines have different slopes, which in standard form means a₁b₂ − a₂b₁ is not zero.

Question 26

Define Linear Model.

Accepted Answer

An equation of the form y = (starting amount) + (constant rate) × x, used when a quantity changes by the same amount for every equal step.

Question 27

Define Initial Value.

Accepted Answer

In a linear model, the output when the input is zero; on a graph it is the y-intercept, and in a word problem it is usually a fixed fee or starting amount.

Question 28

Define Direct Variation.

Accepted Answer

A relationship y = kx in which y is always the same multiple k of x, so its graph is a straight line passing through the origin.

Question 29

Define Linear Inequality in Two Variables.

Accepted Answer

A statement such as y < mx + b or ax + by ≥ c whose solutions are every point in a half-plane on one side of a boundary line.

Question 30

Define Boundary Line.

Accepted Answer

The line separating solutions of a two-variable inequality from non-solutions; it is drawn solid for ≤ or ≥ and dashed for < or >.

Question 31

Define System of Linear Inequalities.

Accepted Answer

Two or more linear inequalities considered together, whose solution set is the overlapping region where all of the shaded half-planes meet.

Question 32

Define Reversing the Inequality Sign.

Accepted Answer

The rule that multiplying or dividing both sides of an inequality by a negative number flips its direction, from less than to greater than or back.

Question 33

Define SAT Algebra Domain.

Accepted Answer

One of the four SAT Math content domains, covering creating and solving linear equations and inequalities, and solving systems of equations using more than one technique.

Question 34

Define Graphing a System in Desmos.

Accepted Answer

Using the Desmos graphing calculator built into the digital SAT's Bluebook app to enter both equations and read their intersection point as the system's solution.