The standard form of a linear equation is Ax+By=C, where A and B are not both 0, and A is nonnegative.
Explain why each equation is not written in standard form. Write the equation in standard form and identify the constants A, B, and C.
3x=−8y+48
−2x+5y=10
12x+y=6
well, of course, the reason for all of them is that they are not written in the required form. Just rearrange the terms as needed.
3x = -8y + 48
3x+8y = 48
clearly, A=3, B=8, C=48
done. Do the others in like wise.
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Equation 1: 3x = -8y + 48
To write this equation in standard form, we need to rearrange the terms so that all variables are on one side and the constants on the other side.
Adding 8y to both sides of the equation, we get:
3x + 8y = 48
Now, this equation is in standard form. The constants A, B, and C are:
A = 3
B = 8
C = 48
Equation 2: -2x + 5y = 10
This equation is already in standard form. The constants A, B, and C are:
A = -2
B = 5
C = 10
Equation 3: 12x + y = 6
To write this equation in standard form, we need to rearrange the terms similarly to equation 1.
Subtracting 6 from both sides of the equation, we get:
12x + y - 6 = 0
Now, this equation is in standard form. The constants A, B, and C are:
A = 12
B = 1
C = -6
To determine whether an equation is in standard form, we need to ensure that it follows the standard form equation: Ax + By = C, where A and B are not both zero, and A is nonnegative.
Let's analyze each equation:
1. 3x = -8y + 48
The given equation is not in standard form because it is not written as Ax + By = C.
To convert it to standard form, we move all the variables (x and y) to one side and leave the constant term (48) on the other side:
3x + 8y = 48
Now the equation is in standard form, where A = 3, B = 8, and C = 48.
2. -2x + 5y = 10
This equation is not in standard form because A, which is the coefficient of x, is negative. We need to make sure that A is nonnegative.
To convert it to standard form, we move the constant term (10) to the other side:
-2x + 5y - 10 = 0
To make A nonnegative, we can multiply the entire equation by -1:
2x - 5y + 10 = 0
Now it is in standard form, with A = 2, B = -5, and C = 10.
3. 12x + y = 6
This equation is not in standard form because there is only one term with a coefficient (y). We need to ensure that both x and y have coefficients.
To convert it to standard form, we rearrange the terms:
12x + y = 6
Now the equation is in standard form, where A = 12, B = 1, and C = 6.
In summary, to determine if an equation is in standard form, we need to ensure that it follows the pattern Ax + By = C, where A and B are not both zero, and A is nonnegative. If the equation is not in standard form, we rearrange the terms by moving variables to one side and constants to the other side.