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21 Cards in this Set

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Is the linear equation 3x +4y =23 equivalent if x=5 and y=2?
Yes the answer is 23 on both sides of the equation.
What is a linear equation with two variables?
An equation that may be written in the form ax + by =c, where the numbers a, b, and c are all real numbers such that a and b are not both, 0.
What are coordinates?
The numbers x and y written in the form (x, y).
What is a dependent variable?
The second element of an ordered pair, usually y.
What is an independent variable?
The first element of an ordered pair, usually x.
What is a number plane?
All points in the plane determined by the intersecting, perpendicular x axis (horizontal axis) and y axis (vertical axis).
What is an origin?
The zero point where the x and y axes intersect in the number plane.
What is a quadrant?
Each of the four regions of the number plane formed by the intersection of the x and y axes.
Define Rectangular coordinate system?
The number plane formed by the intersection of the x and y axes. Also called the Cartesian coordinate system.
Define ordered pair?
Numbers in the form (x, y) that correspond to points in the number plane; also used to write solutions of systems of equations with two variables.
Define x axis?
The horizontal axis in the number plane.
Define y axis?
The vertical axis in the number plane.
Define x intercept?
The x coordinate of the point where the graph crosses the x axis.
Define y intercept?
The y coordinate of the point where the graph crosses the y axis.
Complete the three ordered pair solutions of this equation:

x + y = 5 and your ordered pairs are (3, ) (8, ) (-2, )
x + y = 5
3 + y = 5
3 + y - 3 = 5 - 3 = 2
The first ordered pair is (3, 2).

x + y = 5
8 + y = 5
8 + y - 8 = 5 - 8 = -3
The second ordered pair is (8, -3)

x + y = 5
-2 + y = 5
-2 + y +2 = 5 + 2 = 7
The third ordered pair is (-2, 7)
Complete the three ordered pair
6x - y = 0
Ordered pairs are (3, ) (5, ) (-2, )
6x - y = 0
6(3) - y = 0
18 - y = 0
18 - y + 18 = 0 + 18 = 18
First ordered pair (3, 18)

6x - y = 0
6(5) - y = 0
30 - y = 0
30 - 30 - y = 0 - 30 = -30
-y = -30
-y/-1 = -30/-1 = 30
Second ordered pair is (5, 30)

6x - y = 0
6(-2) - y = 0
-12 - y = 0
-12 + 12 - y = 0 + 12 = 12
-y = 12
-y/-1 = 12/-1= -12
Third ordered pair is (-2, -12)
Complete the three ordered pair solution

9x - 2y = 5
Ordered pairs are (1, ) (0, ) (-3)
9x - 2y = 5
9x - 2y - 9x = 5 - 9x
-2y = 5 - 9x
-2y / -2 = 5 - 9x / -2
y = 5 - 9x /-2
y = 5 - 9(1) /-2
y = 5 - 9 / -2 = 2
First ordered pair is (1, 2)

y = 5 - 9(0) / -2
y = 5 - 0 / -2
y = 5 / -2
Second ordered pair is (0, -5/2)

y = 5 - 9(-3) / -2
y = 5 + 27 / -2
y = 32 / -2
y = -16
The third ordered pair is (-3, -16)
Complete the three ordered pair solution:
x + 2y = 8
Ordered pairs are (3, ) (0, ) (-4, )
x + 2y = 8
3 + 2y = 8
3 -3 + 2y = 8 - 3 =5
2y = 5
2y/2 = 5/2
y=5/2 or 2 1/2
First ordered pair is (3, 0)

x + 2y =8
0 + 2y =8
0 - 0 + 2y = 8 - 0 =0
2y = 8
2y/2 = 8/2=4
y = 4
Second ordered pair is (0, 4)

x + 2y =8
-4 + 2y = 8
-4 + 4 + 2y = 8 + 4
2y = 12
2y/2 =12/2 =6
y = 6
Third ordered pair is (-4, 6)
Complete the three ordered pair solution:
2x - 3y =12
Ordered pairs are (3, ) (0, ) (-3, )
2x - 3y =12
2(3) - 3y =12
6 - 3y =12
6 - 6 -3y = 12 - 6 =6
-3y = 6
-3y/-3 = 6/-3
y = -2
First ordered pair is (3, -2)

2x - 3y = 12
2(0) - 3y =12
-3y = 12
-3y/-3 = 12/-3
y = -4
Second ordered pair is (0, -4)

2x - 3y = 12
2(-3) - 3y =12
-6 + 6 - 3y =12 + 6 =18
-3y = 18
-3y/-3 = 18/-3= -6
Third ordered pair is (-3, -6)
Solve for y in this problem:

6x + y = 15
y = -6x + 15
Complete the three ordered pair with the given equation:
3x - 4y = 24
Ordered pairs are (-4, ) (0, ) (4, )
3x - 4y=24
3(-4) - 4y =24
-12 + 12 - 4y =24 + 12 =36
-4y = 36
-4y/-4 = 36/-4
y = -9
First ordered pair is (-4, -9)

3x - 4y = 24
3(0) - 4y - 24
-4y = 24
-4y/-4 = 24/-4
y = -6
Second ordered pair is (0, -6)

3x - 4y = 24
3(4) - 4y = 24
12 - 12 - 4y = 24 - 12 = 12
-4y = 12
-4y/-4 = 12/-4
y = -3
Third ordered pair is (4, -3)