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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) 