Solving Linear Systems by Substitution

Completing the exercises here is your opportunity to learn by applying the concepts we just discussed.

Show all your work on your own paper. For question 1, check each solution with a “left-side / right-side” check, as demonstrated in class.

Make a real effort to complete each question before opening its answer.

TIP

If you would rather work from paper, use the Print button on this page, or open the handout directly:

OTL - Solving Linear Systems by Substitution

Question 1

Solve each system by substitution. Check solutions using “left-side / right-side”.

a)

$\begin{array}{rl}2x+y& =6\\ 3x+2y& =10\end{array}$

b)

$\begin{array}{rl}x-2y& =4\\ 2x-3y& =7\end{array}$

Answers

a) $(2,2)$

b) $(2,-1)$

Question 2

Solve each system by substitution. Check your final answers.

a)

$\begin{array}{rl}2x+3y& =6\\ x+y& =3\end{array}$

b)

$\begin{array}{rl}2x-y& =13\\ x+2y& =-6\end{array}$

c)

$\begin{array}{rl}4x-y& =3\\ 6x-2y& =5\end{array}$

d)

$\begin{array}{rl}2x-5y& =12\\ x+10y& =-9\end{array}$

Answers

a) $(3,0)$

b) $(4,-5)$

c) $\left(\frac{1}{2},-1\right)$

d) $\left(3,-\frac{6}{5}\right)$

Question 3

Complete the next three linear systems using either graphing or substitution (or both) for additional practice. Check your final answers.

a)

$\begin{array}{rl}x-4y& =8\\ 2x-8y& =8\end{array}$

b)

$\begin{array}{rl}2x-y& =2\\ 3x-2y& =3\end{array}$

c)

$\begin{array}{rl}x+y-4& =0\\ 2x& =8-2y\end{array}$

Answers

a) no solution

b) $(1,0)$

c) infinitely many solutions

Curriculum connection

B1.1

solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination (Sample problem: Solve $y=\frac{1}{2}x-5$, $3x+2y=-2$ for $x$ and $y$ algebraically, and verify algebraically and graphically);

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