Standard Form of a Linear Equation

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Presentation transcript:

Standard Form of a Linear Equation Section 3.1 Standard Form of a Linear Equation

Standard Form of a Linear Equation Standard Form of a Linear Equation Ax + By = C (can also have Ax = C or By = C), A  0, A is nonnegative A and B are not both zero, A, B, and C are integers with a GCF of 1 no fractions or decimals, no negative numbers in front of x

How can 0.5x + 3.2y = 15 be rewritten?

Write each linear equation in Standard Form. a. y – 4x = 9 –4x + y = 9 Put x term first. 4x – y = –9 Cannot start with a neg. Take opp. of both sides.

b. x = y + 8 4( x) = 4(y) + 4(8) Multiply by LCD. 3x = 4y + 32 –4y –4y Eliminate y on right. 3x – 4y = 32

c. 6y = 4x + x 6y = 5x Combine like terms. 5x = 6y Place x term on left. –6y –6y Eliminate y on right. 5x – 6y = 0

d. y + 4 = 11 –4 –4 y = 7

e. 4 – y = 2x + 2y 2x + 2y = 4 – y Place x term on left. +y +y Eliminate y on right. 2x + 3y = 4

Which of the equations is NOT in Standard Form? y = 8 2x = –3 –x + 8y = 11 4x – 5y = –12