Question

RecommendationsSkill plansMathLE Language artsScienceSocial studiesDE TX StandaAlgebra 10.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go toWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Students in a poetry class are writing poems for their portfolios. The teacher wants them towrite stanzas with certain numbers of lines each. Dan wrote 7 short stanzas and 6 longstanzas, for a total of 140 lines. Jim wrote 7 short stanzas and 2 long stanzas, for a total of84 lines. How many lines do the two sizes of stanzas contain?The short stanzas containlines and the long ones containlines.Submit

Answer 1

Short stanzas contains 8 lines

Long stanzas contains 14 lines

Explanations:

Let the number of short stanzas be "x"

Let the number of long stanzas be "y"

If Dan wrote 7 short stanzas and 6 long stanzas, for a total of 140 lines, this is expressed mathematically as:

7x + 6y = 140 ............................ 1

Similarly, if Jim wrote 7 short stanzas and 2 long stanzas, for a total of

84 lines, this is expressed as:

7x + 2y = 84 ......................... 2

Solve both equations simultaneously using elimination method

7x + 6y = 140 ............................ 1

7x + 2y = 84 ......................... 2

Subtract both equations

6y - 2y = 140 - 84

4y = 56

y = 56/4

y = 14

Substitute y = 14 into equaton 1.

Recall that 7x + 6y = 140

7x + 6(14) = 140

7x + 84 = 140

7x = 140 - 84

7x = 56

x = 56/7

x = 8

This shows that the short stanzas contains 8 lines and the long ones contains 14 lines