{"id":"act_quizme:math:q2:07","source_id":"act_quizme","source_item_id":"math-q2-07","external_id":"c6c9246559f9ad9d","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":7,"scored":true,"layout_warning":null,"stem":"Which of the following values, if any, is the y-value of the solution set to the given system of equations? 2x minus y =7 2 x - y = 7 negative 4x+2y =2 - 4 x + 2 y = 2","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><div class=\"item-content\" id=\"p70\">                                                                                  <div>Which of the following values, if any, is the y-value of the solution set to the given system of equations?</div>                                         <ul style=\"list-style-type: none;\">                                                 <li><span class=\"visually-hidden\">2x minus y =7</span><math class=\"srTransform\"><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>7</mn></math></li>                                                 <li><span class=\"visually-hidden\">negative 4x+2y =2</span><math class=\"srTransform\"><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>2</mn></math></li>                                         </ul>                                 </div>                                  </div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>A.</strong> <strong>Incorrect. </strong>You can use elimination or substitution to solve the system of equations. You may have thought the value on the right side of the second equation was a solution to the system.</p><p><strong>B.</strong> <strong>Incorrect.</strong> You can use elimination or substitution to solve the system of equations. You may have thought the difference between the values on the right side of each equation was a solution, <span style=\"white-space: nowrap;\"><math><mn>7</mn><mo>-</mo><mn>2</mn><mo>=</mo><mn>5</mn></math>.</span></p><p><strong>C.</strong> <strong>Incorrect.</strong> You can use elimination or substitution to solve the system of equations. You may have thought the sum of the values on the right side of each equation was a solution to the system, <span style=\"white-space: nowrap;\"><math><mn>7</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>9</mn></math>.</span></p><p><strong>D.</strong> <strong>Correct.</strong> To solve for y, eliminate the x-terms. Start by multiplying both sides of the first equation by 2: <span style=\"white-space: nowrap;\"><math><mn>2</mn><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi></mrow></mfenced><mo>=</mo><mn>2</mn><mfenced><mn>7</mn></mfenced><mo>↔</mo><mn>4</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>14</mn></math>.</span> Then, add the left and right sides of the two equations: <span style=\"white-space: nowrap;\"><math><mfenced><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mn>4</mn><mi>x</mi></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>+</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>14</mn><mo>+</mo><mn>2</mn></mrow></mfenced><mo>↔</mo><mn>0</mn><mo>=</mo><mn>16</mn></math>.</span> Because the resulting equation is false <span style=\"white-space: nowrap;\">(<math><mn>0</mn><mo>≠</mo><mn>16</mn></math>),</span> there is no solution to the system of equations and therefore no such value for <span style=\"white-space: nowrap;\"><math><mi>y</mi></math>.</span></p>","correct_answer":["D"],"equiv_key":"66907cf32670f2f9a04ee121","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>2</p>","ord":0},{"label":"B","content_html":"<p>5</p>","ord":1},{"label":"C","content_html":"<p>9</p>","ord":2},{"label":"D","content_html":"<p>There is no such value for y.</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78},"equivalents":[]}