Algebra 1 Common Core Student Edition, Grade 8-9

@40.Writing Let a be any real num ber. Will th e system at th e right

always, sometimes, or never have a solution? Explain.

y — ax

y = ax + 4

@41.Reasoning Explain h o w y o u can use su b stitu tio n y + x = x

to show th a t the system at th e right h as no solution. ^ = 4

Challenge 42. Agriculture A farm er grows corn, tom atoes, an d sunflowers o n a 320-acre farm.
This year, th e farm er w ants to p la n t twice as m an y acres of to m ato es as acres of
sunflowers. The farm er also w ants to p la n t 40 m ore acres of corn th a n of tom atoes.
How m any acres of each crop should th e farm er plant?

43. Track and Field M ichelle an d Pam are ru n n in g a 200-m race. M ichelle ru n s at an
    average of 7.5 m /s. Pam averages 7.8 m /s, b u t she starts 1 s after Michelle.
    a. How long will it take Pam to catch u p to Michelle?
    b. Will P am overtake M ichelle before th e finish line? Explain.

Look back at th e inform ation on page 363 a b o u t th e a m o u n ts of tim e Ashley

uses the stair m ach in e a n d rowing m ach in e at th e gym.

a. Define two variables to re p resen t th e a m o u n ts of tim e Ashley can sp en d o n th e two

exercise m achines.

b. W rite a system of two eq u atio n s th a t describes th e relationships b etw een the

am o u n ts of tim e Ashley sp en d s o n th e two m achines.

c. Solve th e system of equations.

d. Interpret the solution of the system.

Apply What You've Learned

M P 1, M P 4

c -V

| L e s s o n 6 2 Solving Systems Using Substitution^377