Mathematics

Question

Linear system word problem
Linear system word problem

1 Answer

  • Answer:

    1 year

    Step-by-step explanation:

    Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.

    In this problem, "m" is the rate of growth in inches per year.

    "b" is the starting height.

    let "x" be the number of years

    let "y" be the height in inches

    Tree A: y = 8x + 3

    Tree B: y = 9x + 2

    Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.

    8x + 3 = 9x + 2

    8x + 3 - 3 = 9x + 2 - 3      Subtract 3 from both sides

    8x = 9x - 1

    8x - 9x = 9x - 9x - 1     Subract 9x form both sides

    -x = -1       Divide both sides by -1 to isolate

    x = 1         Number of years for the trees to be the same height

    Therefore it will take 1 year for the trees to be the same height.

    If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.

    y = 8x + 3

    y = 8(1) + 3

    y = 11     Number of inches when trees are the same height

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