Question

which of the following is a first - degree equation in two variables?
a. $3x - 2y = 5$
b. $x^{2}+y = 1$
c. $x - 3 = 2x$
d. $\frac{1}{x}+5y = 6$

Explanation:

Step1: Recall definition

A first-degree (linear) equation in two variables has the form $Ax + By = C$, where $A,B,C$ are constants, $A,B
eq0$, and variables have exponent 1, no variable in denominator.

Step2: Analyze Option A

Check $3x - 2y = 5$: two variables $x,y$, each to the 1st power, no denominators with variables. Fits the definition.

Step3: Analyze Option B

Check $x^2 + y = 1$: $x$ has exponent 2, so it is second-degree. Reject.

Step4: Analyze Option C

Check $x - 3 = 2x$: simplifies to $-x -3=0$, only one variable $x$. Reject.

Step5: Analyze Option D

Check $\frac{1}{x} + 5y = 6$: $x$ is in the denominator (equivalent to $x^{-1}$), so not first-degree. Reject.

Answer:

A. $3x - 2y = 5$