| The model below represents the system of equations: | 2x − 2y = -1 |
| x + 2y = 4 |
What is the solution?
A. (3, .5)
Incorrect. In the model 3x = 3, so each of the units need to be divided up among the x’s.
B. (1, 1.5)
Correct! Each x (rectangle) gets one unit.
C. (1, 2)
Incorrect. Try plugging in 1 for the x-value to solve for y.
D. (1.5, 1)
Incorrect. The rectangles represented the x-value.
| How would the model of the second equation change to eliminate x from this system of linear equations below? | 4x + 5y = 8 |
| 2x − 3y = -18 |
A.
Incorrect. The units would also need to be doubled and change signs.
B.
Incorrect. All objects need to be doubled for the equation to remain equivalent. Plus, you can’t change only one sign without changing all of them. It’s like multiplying by negative one.
C.
Incorrect. You need to have 4 negative x rectangles.
D.
Correct! You doubled each of the figures and change their signs.
| What is the y-coordinate of the solution to the system of linear equations below? | 4x + 5y = 8 |
| 2x − 3y = -14 |
A.
Incorrect. You forgot to double and change the sign of the -14.
B.
Incorrect. You forgot to change the sign.
C.
Correct! You doubled each and changed the sign. That’s like multiplying by a -2. Good job!
D.
Incorrect. You need to double and change the sign of all three quantities on the second row.
Which problem statement best represents this model?
A. Javier and Kevin walked 4 miles per day. If they walked 22 miles all together, how many miles did Kevin walk?
Incorrect. The first part of the model means Javier walked 4 more miles than Kevin.
B. JiWoo has 4 more candies than her sister, Kyon. If there are 22 total candies, how many candies belonged to Kyon?
Correct! You noticed the equal sign placement.
C. Jeremy and Kandice are blowing up balloons. Kandice popped 4 balloons. They have inflated 22 balloons together. How many balloons has Jeremy popped?
Incorrect. Popped would be negative.
D. Katy and Jack were selling lemonade at $4 per gallon. If Katy and Jack sold 22 gallons together, how many gallons of lemonade did Jack sell?
Incorrect. The first part means that Jack sold 4 more than Katy.
Julia has 4 more candies than her sister, Kiera. If there are 22 total candies, how many candies belonged to Kiera?
A. 26
Incorrect. Subtract 4 from both sides, and divide the remaining between the two Ks.
B. 13
Incorrect. Subtract 4 from both sides.
C. 18
Incorrect. 2K = 18. Divide the 18 between the two Ks.
D. 9
Correct! You solved by substitution of models.