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
