Exercise 117 Page 324

Create two equations describing the number of students in each high school, then combine them to form a system of equations.

In 7 years

Practice makes perfect

Both high schools' numbers of students change with a constant rate. This means we can describe the number of students with linear functions in slope-intercept form. y= mx+ b In this form m is the slope and b is the y-intercept. In this case the y-intercept shows the high school's current number of students, which is b= 839 and b= 1644 for Tehachapi and Fresno, respectively. Tehachapi:& y= mx+ 839 Fresno:& y= mx+ 1644 We also have to determine the slope. For Tehachapi the population increases by 34 people per year, which translates to a slope of m= 34. Conversely, in Fresno the population decreases by 81 per year, which can be interpreted as a slope of m= - 81. With this information we can complete the equations. Tehachapi:& y= 34x+ 839 Fresno:& y= - 81x+ 1644 If we combine the equations, we get a system of equations. y=34x+839 y=- 81x+1644 By solving this system we can determine how many years it will take for the number of students to be the same. Note that both equations are solved for y, and therefore we should use the Substitution Method.

y=34x+839 & (I) y=- 81x+1644 & (II)

Substitute

(II): y= 34x+839

y=34x+839 34x+839=- 81x+1644

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(II): Solve for x

AddEqn

(II): LHS+81x=RHS+81x

y=34x+839 115x+839=1644

SubEqn

(II): LHS-839=RHS-839

y=34x+839 115x=805

DivEqn

(II): .LHS /115.=.RHS /115.

y=34x+839 x=7

After 7 years the high schoolss numbers of students will be the same.

Extra

Why didn't we calculate y?

Note that we are only looking to determine when the number of students are the same and not what the number of students are at that time. Therefore, we do not have to solve for y.