Name:
Ms. D’Amato
Date:
Block:
Solving Linear Systems by Graphing
An ordered pair that makes a linear equation TRUE is called a __________________
To solve a system of linear equations, you have to find an ordered pair that
________________________________________________.
Steps:
1.
2.
3.
Example:
Put the equations in slope-intercept form or standard form. Graph.
Locate the point of intersection and write it down.
Verify that the point makes both equations true!!
2
x2
3
y  x  3
y
Point:
Verify:
Example:
Point:
Verify:
y  x 1
y  x  3
Example:
2x  y   4
2x  y  4
Point:
Verify:
Example:
7 y   14 x  42
7 y  14 x  14
Point________
Verify:
Special case #1:
The lines have the same slope (but not the same y-intercept). They are _______ lines.
Since they do not intersect and share ____ points, there is ____________________.
Test each pair of lines to determine if they are parallel.
1.
y = 3x + 2
y = 3x − 5
2.
y + 2x = 2
y = 2x − 5
3.
x + 2y = 6
3x + 6y = 12
Special case #2:
The lines have the same slope and the same y-intercept. They are actually the SAME
line. They will share ___________________________.
Put both of these equations into slope-intercept form. What do you notice?
Example:
a.) y + 2x = 3
b.) 2y = −4x + 6
x y  3
x y  3
Example:
 2 y  4 x  6
y  2x  3
Try these:
1.
y  x 1
y  2x  2
Point:
Verify:
2.
y  x2
y  x
Point:
Verify:
3.
y4
y  2x
Point:
Verify:
4.
2x  y  4
3x  y  6
Point:
Verify:
5.
 3x  2 y  6
x y  3
Point:
Verify:
One more time:
Different slope
Same slope; Different y-int
Both slope and y-int the same
Rental Business A business rents in-line skates and bicycles. During one day, the business has
a total of 25 rentals and collects $450 for the rentals. In-line skates cost $15 per day and
bicycles cost $30 per day. Find the number of pairs of skates rented and the number of
bicycles rented.