Solving Linear Systems Graphically

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

NOTE

As mentioned in class, complete “every other” question given below.

You can save the questions you do not complete now to prepare for future evaluations.

Solve each system by graphing on grid paper. For at least three questions, do 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 Graphically

Question 1

Solve each system by graphing. Check your solutions.

a)

$\begin{array}{rl}y& =x-1\\ y& =9-x\end{array}$

b)

$\begin{array}{rl}y& =x+3\\ y& =1-x\end{array}$

c)

$\begin{array}{rl}y& =2x+1\\ y& =x-2\end{array}$

d)

$\begin{array}{rl}y& =1-2x\\ y& =x-5\end{array}$

Answers

a) $(5,4)$

b) $(-1,2)$

c) $(-3,-5)$

d) $(2,-3)$

Question 2

Solve each system by graphing. Check your solutions.

a)

$\begin{array}{rl}x-y& =-5\\ x+y& =1\end{array}$

b)

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

c)

$\begin{array}{rl}3x-2y& =12\\ x-2y& =8\end{array}$

d)

$\begin{array}{rl}2x+3y& =-12\\ 2x-y& =-4\end{array}$

Answers

a) $(-2,3)$

b) $(2,0)$

c) $(2,-3)$

d) $(-3,-2)$

Question 3

Solve each system by graphing. Check your solutions.

a)

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

b)

$\begin{array}{rl}x+y& =5\\ x-y& =-7\end{array}$

c)

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

d)

$\begin{array}{rl}x+3y& =-1\\ 2x+6y+2& =0\end{array}$

e)

$\begin{array}{rl}2x+y& =12\\ 3x-2y& =18\end{array}$

f)

$\begin{array}{rl}2x+y& =-2\\ 4x& =y-16\end{array}$

g)

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

h)

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

i)

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

j)

$\begin{array}{rl}3x+y& =-11\\ y& =2x+4\end{array}$

k)

$\begin{array}{rl}3x+4y-16& =0\\ x-2y-2& =0\end{array}$

l)

$\begin{array}{rl}3x& =y+8\\ 6x-2y-1& =0\end{array}$

m)

$\begin{array}{rl}2x+3y& =7\\ 2x-3y& =13\end{array}$

n)

$\begin{array}{rl}y& =\frac{1}{2}x+3\\ x& =2y-6\end{array}$

o)

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

p)

$\begin{array}{rl}3x+2y-10& =0\\ 2x-3y+2& =0\end{array}$

Answers

a) $(3,-1)$

b) $(-1,6)$

c) $(4,-1)$

d) infinitely many solutions

e) $(6,0)$

f) $(-3,4)$

g) no solution

h) $(-2,-1)$

i) $(2,-1)$

j) $(-3,-2)$

k) $(4,1)$

l) no solution

m) $(5,-1)$

n) infinitely many solutions

o) $(-1,-2)$

p) $(2,2)$

Curriculum connection

B1.5

represent the equations of lines in different forms (e.g., $y=mx+b$, $Ax+By+C=0$, $Ax+By=D$) and translate between these forms, as appropriate for the context.

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