Liam wants to buy a car and pay for it in three installments. The total cost of the car is $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

9514 1400 393

  see below

Step-by-step explanation:

We assume the values of the installment payments are the values before interest is added. The given relations are ...

  x + y + z = 29000 . . . . . . the total of the 3 installments is the price of the car

  2x = 1000 +z +3y . . . . . . the 1st is $1k more than the 3rd and twice the 2nd

  0.15(y +z) = 2100 . . . . . . 15% interest on the last two installments totals 2100

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We want to rearrange each of these equations to standard form:

  x + y + z = 29000

  2x -3y -z = 1000

  0x + 0.15y +0.15z = 2100

Putting these coefficients into augmented matrix form, we have ...

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The installments (before interest) are (x, y, z) = (15000, 7500, 6500) dollars.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

d. vertex

step-by-step explanation: