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How many solutions are possible if a geometric representation is of three parallel planes?<\/p>\n","answers":["

There are no solutions<\/p>\n","

There is a unique set of solutions<\/p>\n","

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There are three unique solutions<\/p>\n"]},{"subContentId":"0628f4f4-cd3b-4405-936e-2f5ec27177b8","question":"

How many solutions are possible if a geometric representation is of two parallel planes that are intersected by a third plane?<\/p>\n","answers":["

There are no solutions<\/p>\n","

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There is a unique set of solutions<\/p>\n","

There are no solutions<\/p>\n","

There are multiple solutions<\/p>\n","

There are three unique solutions<\/p>\n"],"question":"

How many solutions are possible if a geometric representation is of three planes that intersect at a single point?<\/p>\n"},{"subContentId":"6eddd32e-d859-453c-b162-21f1bf273067","answers":["

There are multiple solutions<\/p>\n","

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How many solutions are possible if a geometric representation is of three planes that perfectly overlap each other?<\/p>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"autoContinue":true,"timeoutCorrect":2000,"timeoutWrong":3000,"soundEffectsEnabled":true,"enableRetry":true,"enableSolutionsButton":true,"passPercentage":100},"l10n":{"nextButtonLabel":"Next question","showSolutionButtonLabel":"Show solution","retryButtonLabel":"Retry","solutionViewTitle":"Solution list","correctText":"Correct!","incorrectText":"Incorrect!","muteButtonLabel":"Mute feedback sound","closeButtonLabel":"Close","slideOfTotal":"Slide :num of :total","scoreBarLabel":"You got :num out of :total points","solutionListQuestionNumber":"Question :num","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again."}},"subContentId":"592e359f-f6bf-44fc-bdf4-72d24a48a611","metadata":{"contentType":"Single Choice Set","license":"U","title":"node-9850__3x3 Interactive video MCQ1"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":true,"seekTo":41,"message":"

It looks like you need a little more pratice with teh different geometric representations. Watch the explanation again.<\/p>\n","seekLabel":"Try again."},"requireCompletion":false},"label":"

Select the button to test your understanding!<\/p>\n"},{"x":42.5764192139738,"y":50.48543689320388,"width":10,"height":10,"duration":{"from":482.758,"to":492.758},"libraryTitle":"Single Choice Set","action":{"library":"H5P.SingleChoiceSet 1.11","params":{"choices":[{"subContentId":"47465982-1717-4f86-be51-eedad4e75ff8","question":"

Solve this system of simultaneous equations:<\/p>\n\n

x <\/em>+ y <\/em>+ z <\/em>= 6<\/p>\n\n

3x<\/em> - y<\/em> + 2z<\/em> = 18<\/p>\n\n

2x<\/em> + 2y<\/em> - z<\/em> = 0<\/p>\n","answers":["

x<\/em> = 3, y <\/em>= -1, z <\/em>= 4 <\/p>\n","

There are no solutions<\/p>\n","

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Solve this system of simultaneous equations:<\/p>\n\n

3x<\/em> - y <\/em>+ z <\/em>= 4 <\/p>\n\n

x <\/em>+ 5y<\/em> - 3z<\/em> = 23<\/p>\n\n

2x<\/em> + 2y<\/em> - z<\/em> = 10<\/p>\n","answers":["

There are no solutions<\/p>\n","

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x <\/em>= 0, y <\/em>= -4, z <\/em>= 0<\/p>\n","

x <\/em>= 1, y<\/em> = -2, z<\/em> = -12<\/p>\n"]},{"subContentId":"1a6299cb-6579-4438-b2b4-c4554a668cd0","question":"

Solve this system of simultaneous equations:<\/p>\n\n

4x<\/em> - y<\/em> + 2z<\/em> = 5<\/p>\n\n

x <\/em>+ 3y<\/em> - 5z<\/em> = 4<\/p>\n\n

6x<\/em> + 5y<\/em> - 8z<\/em> = 13 <\/p>\n","answers":["

There are multiple solutions<\/p>\n","

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x <\/em>= 1, y <\/em>= 1, z <\/em>= 1 <\/p>\n"]},{"subContentId":"30f9f009-4e74-4cea-8c93-2942bd6c0e91","question":"

Solve this system of simultaneous equations:<\/p>\n\n

x <\/em>+ 2y <\/em>+ z <\/em>= 2<\/p>\n\n

x <\/em>+ y <\/em>+ 2z <\/em>= 3<\/p>\n\n

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x<\/em> = -5, y<\/em> = 2, z<\/em> = 3<\/p>\n","

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It looks like you need to see the example of how to solve simultatneous equation again.<\/p>\n","seekLabel":"Have another go!"},"requireCompletion":false},"label":"

Select this button to check your understanding!<\/p>\n"}]},"summary":{"task":{"library":"H5P.Summary 1.10","params":{"intro":"

Choose the correct statement from each set.<\/p>\n","summaries":[{"subContentId":"670b713d-4421-43bc-954e-6b06c10e429e","tip":"","summary":["

Three planes must all intersect at at least one point for a system of three equations to have at least one solution.<\/p>\n","

When at least two planes are parallel, there will be at least one solution for a system of three equations.<\/p>\n","

When three planes intersect at a common line, there will be a single, unique solution for the system of three equations.<\/p>\n"]},{"subContentId":"3dcb6956-a90c-4810-947f-9a95a4961f18","summary":["

When using the subsitution method to solve simultaneous equations, first rearrange one equation to make a pronumeral the subject. Then replace that pronumeral in the other two equation with the rearranged equation.<\/p>\n","

When solving systems of three equations, you must use the substitution method. The elimination method only works for systems of two equations.<\/p>\n"],"tip":""}],"overallFeedback":[{"from":0,"to":100}],"solvedLabel":"Progress:","scoreLabel":"Wrong answers:","resultLabel":"Your result","labelCorrect":"Correct.","labelIncorrect":"Incorrect! Please try again.","alternativeIncorrectLabel":"Incorrect","labelCorrectAnswers":"Correct answers.","tipButtonLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","progressText":"Progress :num of :total"},"subContentId":"61631c23-ea5f-4642-9e62-9175af7820c5","metadata":{"contentType":"Summary","license":"U","title":"node-9850__3x3 Interactive video Summary"}},"displayAt":3}},"override":{"autoplay":false,"loop":false,"showBookmarksmenuOnLoad":false,"showRewind10":false,"preventSkipping":false,"deactivateSound":false},"l10n":{"interaction":"Interaction","play":"Play","pause":"Pause","mute":"Mute, currently unmuted","unmute":"Unmute, currently muted","quality":"Video Quality","captions":"Captions","close":"Close","fullscreen":"Fullscreen","exitFullscreen":"Exit Fullscreen","summary":"Open summary dialog","bookmarks":"Bookmarks","endscreen":"Submit screen","defaultAdaptivitySeekLabel":"Continue","continueWithVideo":"Continue with video","more":"More player options","playbackRate":"Playback Rate","rewind10":"Rewind 10 Seconds","navDisabled":"Navigation is disabled","sndDisabled":"Sound is disabled","requiresCompletionWarning":"You need to answer all the questions correctly before continuing.","back":"Back","hours":"Hours","minutes":"Minutes","seconds":"Seconds","currentTime":"Current time:","totalTime":"Total time:","singleInteractionAnnouncement":"Interaction appeared:","multipleInteractionsAnnouncement":"Multiple interactions appeared.","videoPausedAnnouncement":"Video is paused","content":"Content","answered":"@answered answered","endcardTitle":"@answered Question(s) answered","endcardInformation":"You have answered @answered questions, click below to submit your answers.","endcardInformationOnSubmitButtonDisabled":"You have answered @answered questions.","endcardInformationNoAnswers":"You have not answered any questions.","endcardInformationMustHaveAnswer":"You have to answer at least one question before you can submit your answers.","endcardSubmitButton":"Submit Answers","endcardSubmitMessage":"Your answers have been submitted!","endcardTableRowAnswered":"Answered questions","endcardTableRowScore":"Score","endcardAnsweredScore":"answered","endCardTableRowSummaryWithScore":"You got @score out of @total points for the @question that appeared after @minutes minutes and @seconds seconds.","endCardTableRowSummaryWithoutScore":"You have answered the @question that appeared after @minutes minutes and @seconds seconds.","videoProgressBar":"Video progress"}}