Name:
Date: ______________
Algebra 2
Solving Linear Systems Graphically
Solving Linear Systems Graphically
One way to solve a linear system is to solve graphically. When you have two linear equations relating
x and y, you can make the line graph of each equation. Find the intersection point of the two lines, and
its (x, y) coordinates give the solution. Some notes about this method:
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The graphing could be done either on paper or by calculator.
Solving each equation for y is often needed before graphing on paper and always needed before
calculator graphing, so that’s usually the step that immediately follows writing the system.
If you have a choice between using fractions and using rounded-off decimals, you’ll get better
accuracy using the fractions.
On the calculator, use [2nd][TRACE]Intersect to find the intersection point.
You try it
1. In basketball, some baskets are worth 3
points and others are worth 2 points.
Suppose that a player makes 7 baskets, and
scores a total of 18 points.
How many of the baskets were three-point
baskets, and how many were two-point
baskets?
Variables:
Let x= the number of 2 point baskets
y= the number of 3 point baskets
Write a system of equations:
Solve this system using graphing on paper:
Answer:______________________
Name:
Date: ______________
2. Solve this system using calculator graphing.
2.3x + 5.8y = 18.5
6.1x – 1.7y = 14.9
Algebra 2
Solving Linear Systems Graphically
Name:
Date: ______________
3. Solve these systems by graphing on paper.
a. y = 4x – 5, y = – 12 x + 4
b. 2x – 3y = 7, –x + 2y = –5
c. 3x  y  8,

1
1
x  y 1
3
6

d. y = 3x + 1; 6x – 2y = –2
Algebra 2
Solving Linear Systems Graphically
Name:
Date: ______________
Algebra 2
Solving Linear Systems Graphically
4. Solve this system using calculator graphing:
5x – 4y = 129,
–6x –10y = 82.
5. Solve this word problem by writing a linear system and solving it graphically by calculator.
You have some quarters and some nickels in your pocket.
In total, you have 7 coins, and together they are worth 95 cents.
How many are nickels and how many are quarters?
Name:
Date: ______________
Algebra 2
Solving Linear Systems Graphically
6. Solve this word problem by writing a linear system and solving it graphically on paper.
A sub sandwich shop sells small subs and large subs.
One customer buys 1 small sub and 2 large subs for $10.
Another customer buys 2 small subs and 1 large sub for $8.
What are the prices for a small sub and a large sub?