1
\begin{cases} 5m - 4n = 10a - 4 \\[2.5mm] m - 2na = 0 \end{cases}
Chapter 20 · Linear Systems
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From Literal Equations in Two Variables, exercise 3
Treat a, b, c, d (and these letters with subscripts) as known numbers; solve for the other letters and check. In Exercises 17–20 solve for x and y.
From Problems with Letters, exercise 11
Solve each problem. The answers are expressions in the letters.
2
The altitude of a triangle is a feet, the base is b feet. The altitude is increased h feet and the base decreased so that the area is the same as before. How many feet are taken from the base?
From Problems in Two Unknowns, exercise 2
State two equations in two unknowns, using the first letter of each unknown's name, and solve.
3
The quotient of two numbers is 6 and their sum is 49. Find the numbers.
From Solving by Substitution, exercise 11
Solve by the method of substitution.
4
\begin{cases} \dfrac{1}{7 + 2m_1} = \dfrac{-7}{m_2 - 1} \\[2.5mm] m_1 = m_2 + 3 \end{cases}
From Problems in Three and Four Unknowns, exercise 6
State three equations in three unknowns (four in four) and solve.
5
The sum of three numbers is 26. The quotient of two of them is 9, and the sum of these two divided by the third is 3\frac13. Find the numbers.
From More Problems in Two Unknowns: Work, Streams, and Trains, exercise 27
State two equations in two unknowns and solve.
6
The difference of the reciprocals of two numbers is 1\frac16. The quotient of the greater number divided by the less is 1\frac78. Find the numbers.
From Systems in Three and Four Variables, exercise 5
Solve each system.
7
\begin{cases} 2m + 3n - 4p = -3 \\[2.5mm] m + n + 3p = -9 \\[2.5mm] m + 2n - 7p = 6 \end{cases}
From More Problems with Letters: Money, Work, and Motion, exercise 29
Solve each problem. The answers are expressions in the letters.
8
A works h times as fast as B. Together they can do a piece of work in 4 days. How many days would each require alone?
From Systems Containing Fractions, exercise 15
Solve each system and check.
9
\begin{cases} \dfrac{1}{m_1} + \dfrac{1}{m_2} = \dfrac{2}{15} \\[2.5mm] \dfrac{1}{m_1} - \dfrac{1}{m_2} = -\dfrac13 \end{cases}
From Systems: Solving by Addition or Subtraction, exercise 12
Solve each system and check.
10
\begin{cases} 5x - 3w = 2 \\[2.5mm] 15x + 12w = -5 \end{cases}