(x, y)$ represent in simultaneous equations?","back":"The single pair of values that makes both equations true at the same time.","points":1},{"id":"ed63922e-53fe-4eb8-bacd-37580d00a6bb","cardType":"basic","front":"How do you verify if a coordinate like $(4, 1)$ is the solution to a system of equations?","back":"Substitute the values into both equations to see if they hold true.","points":2},{"id":"09001819-a458-40bd-b7f2-56e53be2da83","cardType":"cloze","front":"To eliminate a variable with [ ] signs (e.g. $+3y$ and $-3y$), you add the equations together.","back":"To eliminate a variable with opposite signs (e.g. $+3y$ and $-3y$), you add the equations together.","points":null},{"id":"5009b2f6-ddc0-48ad-8aa9-e9205828c42c","cardType":"cloze","front":"To eliminate a variable with [ ] sign (e.g. $2x$ and $2x$), you subtract one equation from the other.","back":"To eliminate a variable with the same sign (e.g. $2x$ and $2x$), you subtract one equation from the other.","points":null},{"id":"c6e10f3f-9d84-492b-afb1-c4f70743bca5","cardType":"basic","front":"What is a coefficient in an algebraic term like $4x$?","back":"The number multiplying the variable (the 4).","points":1},{"id":"1af192ce-822f-43a3-9439-4357896baf4d","cardType":"basic","front":"When subtracting equations, what is the result of $5y - (-y)$?","back":"$$6y$","points":1},{"id":"78257a11-b3e4-4519-97c2-ee333dee2807","cardType":"basic","front":"If neither variable has a matching coefficient, how can you prepare the equations for elimination?","back":"Multiply one (or both) whole equations by a constant to make one coefficient match.","points":2},{"id":"e995f73c-b4fc-4a3e-b6f7-1e7412e745b4","cardType":"basic","front":"What is the common mistake when multiplying an equation to match coefficients?","back":"Forgetting to multiply every term on both sides of the equals sign.","points":1},{"id":"29aa0d31-30e9-4ddc-95bf-f6ef31aa316b","cardType":"basic","front":"Define standard form for linear simultaneous equations.","back":"$$ax + by = c$, where $x$ and $y$ terms are on the left and the constant is on the right.","points":1},{"id":"485441ad-d320-4017-9f0e-59b20f3063f2","cardType":"cloze","front":"The standard form of $3x = 10 + y$ is $\\text{[...]}$.","back":"The standard form of $3x = 10 + y$ is $\\boxed{3x - y = 10}$.","points":null},{"id":"6f609683-2281-49fc-944b-a652ac8163d3","cardType":"basic","front":"How can you simplify an equation containing decimals (e.g., 4.5) before solving?","back":"Multiply the whole equation by 10 to clear the decimal point.","points":1},{"id":"8051a9b3-b954-49af-aca3-325b3315b665","cardType":"cloze","front":"If an equation contains 4.5, multiplying the whole equation by 10 changes it to [ ].","back":"If an equation contains 4.5, multiplying the whole equation by 10 changes it to 45.","points":null},{"id":"190ec7e1-f47f-4fc5-a8e8-0ddd11fef511","cardType":"basic","front":"What is the very first step when solving a word problem using simultaneous equations?","back":"Define variables (assign letters) for the unknown values.","points":1},{"id":"538aa107-51f4-4057-ab07-04ce8fd0fa0c","cardType":"basic","front":"If you solve a word problem using pence, but the question asks for prices, what must you remember?","back":"Convert the final answers back into pounds (£).","points":1},{"id":"d6a8a4c5-04ab-4279-9392-857424a2ce6d","cardType":"basic","front":"After using elimination to find

Simultaneous Equations Flashcards

Simultaneous Equations Flashcards

Simultaneous Equations Flashcards

Simultaneous Equations Flashcards