To find the point of intersection, substitute to find the other value. Substitute = 1 into = + 1 and write the answer for and as an ordered pair. y x x y −3y To test the solution, substitute = and = 1 into 4x 3y = to verify that it x y −2 − −11 makes the equation true. 3(1) = the solution must be correct. Since 4(−2) − −11, 6-50. Camila is trying to find the equation of a line that passes through the points (−1, 16) and (5, 88). Does the equation = 12x + 28 work? Justify your y answer. (Desmos). 6-51. Solve the systems of equations below using the method of your choice. Check your solutions, if possible. = 7 2x y − 2x + = 10 y 3y 1 = x − 4x 2y = 16 − Hotdogs and corndogs were sold at last night's football game. Use the 6-52. information below to write mathematical sentences to help you determine how many corndogs were sold. a.The number of hotdogs sold was three fewer than twice the number of corndogs. Write a mathematical sentence that relates the number of hotdogs and corndogs. Let represent the number of hotdogs and represent the number of corndogs. h c b.A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write a mathematical sentence to represent this information. How many corndogs were sold? Show how you found your answer.
To find the point of intersection, substitute to find the other value. Substitute y = 1 into x = −3y + 1 and write the answer for x and y as an ordered pair. To test the solution, substitute x = −2 and y = 1 into 4x − 3y = −11 to verify that it makes the equation true. Since 4(−2) − 3(1) = −11, the solution must be correct. 6-50. Camila is trying to find the equation of a line that passes through the points (−1, 16) and (5, 88). Does the equation y = 12x + 28 work? Justify your answer. (Desmos). 6-51. Solve the systems of equations below using the method of your choice. Check your solutions, if possible. y = 7 − 2x 2x + y = 10 3y − 1 = x 4x − 2y = 16 6-52. Hotdogs and corndogs were sold at last night's football game. Use the information below to write mathematical sentences to help you determine how many corndogs were sold. a.The number of hotdogs sold was three fewer than twice the number of corndogs. Write a mathematical sentence that relates the number of hotdogs and corndogs. Let h represent the number of hotdogs and c represent the number of corndogs. b.A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write a mathematical sentence to represent this information. How many corndogs were sold? Show how you found your answer.
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