Question

which equations are in standard form? select all that apply. a) 3x + 12y = -6 b) x - y = 1 c) 2x = 9 d) -10x + 7y = 13 e) 6y = 11 f) $\frac{3}{4}x + y = 8$ g) 5x + 14y = 3

Explanation:

Step1: Recall standard - form of linear equation

The standard form of a linear equation is $Ax + By=C$, where $A$, $B$, and $C$ are integers, and $A\geq0$.

Step2: Analyze option A

For $3x + 12y=-6$, $A = 3$, $B = 12$, $C=-6$, which is in standard form.

Step3: Analyze option B

For $x - y=1$, $A = 1$, $B=-1$, $C = 1$, which is in standard form.

Step4: Analyze option C

For $2x=9$, it can be written as $2x+0y = 9$, $A = 2$, $B = 0$, $C = 9$, which is in standard form.

Step5: Analyze option D

For $- 10x+7y = 13$, although it is a linear equation, $A=-10<0$. To be in standard - form with $A\geq0$, we can multiply the entire equation by $-1$ to get $10x - 7y=-13$. But as it is given, it is not in standard form according to the strict definition with $A\geq0$.

Step6: Analyze option E

For $6y = 11$, it can be written as $0x+6y = 11$, $A = 0$, $B = 6$, $C = 11$, which is in standard form.

Step7: Analyze option F

For $\frac{3}{4}x + y=8$, $A=\frac{3}{4}$ is not an integer, so it is not in standard form.

Step8: Analyze option G

For $5x + 14y=3$, $A = 5$, $B = 14$, $C = 3$, which is in standard form.

Answer:

A. $3x + 12y=-6$, B. $x - y = 1$, C. $2x = 9$, E. $6y = 11$, G. $5x + 14y=3$