Linear Equations

For the problem described on card #9, what is a combination that satisfies the solution but is not a realistic solution to the problem?

Any odd number of chocolate bars sold would result in a decimal number of gummy bears sold. These value would satisfy the equation but not be possible in reality given that you can only sell whole numbers of physical things.

Does the ordered pair (3, 2) satisfy the equation 4x + 5y = 20?

No 4(3) + 5(2) = 20 12 + 10 = 20 22 ≠ 20

Is the equation 12x² + 8y = 48 a linear equation?

No, because the x variable is squared so it can't be written in the form Ax + By = C.

Find an ordered pair that satisfies the equation 5x + 2y = 30. There are many answers here.

Possible (but not all) answers (0, 15), (1, 12. 5), (2, 10), (3, 7.5), (4, 5), (5, 2.5), (6, 0)

Does the ordered pair (1, 7) satisfy the equation 7x − 4y = -21

Yes 7(1) −4(7) = -21 7 - 28 = -21 -21 = -21

Is the equation y = -4x + 17 a linear equation?

Yes, because it could be written in the form Ax + By = C. (4x + y = 17)

Is the equation 5x + 7y = 12 a linear equation?

Yes, because it is written in the form Ax + By = C

A school fundraiser sells chocolate bars for $2 a piece and a bag of gummy bears for $4 a piece. Each student needs to raise a total of exactly $60 selling candy. Write an equation that represents all possible combinations of candy bars and gummy bears that would result in $60.

x = # of chocolate bars sold y = # of bags of gummy bears sold 2x + 4y = 60

Find the x- and y-intercepts of the equation 6x + 4y = 48.

x-intercept (y = 0) 6x + 4(0) = 48 6x = 48 x = 8 y-intercept (x = 0) 6(0) + 4y = 48 4y = 48 y = 12 x-intercept (8, 0) & y-intercept (0, 12)

Find the x- and y-intercepts of the equation 8x + 3y = 15.

x-intercept (y = 0) 8x + 3(0) = 15 8x = 15 x = 1 7/8 y-intercept (x = 0) 8(0) + 3y = 15 3y = 15 y = 5 x-intercept (1 7/8, 0) & y-intercept (0, 5)