Question

how many solutions does the system of equations below have? 3x - 10y = 3 -x - 4y = -14 no solution one solution infinitely many solutions

Explanation:

Step1: Isolate $x$ from second equation

From $-x - 4y = -14$, rearrange to get $x = 14 - 4y$.

Step2: Substitute $x$ into first equation

Substitute $x = 14 - 4y$ into $3x - 10y = 3$:
$$3(14 - 4y) - 10y = 3$$

Step3: Simplify and solve for $y$

Expand and combine like terms:
$$42 - 12y - 10y = 3$$
$$42 - 22y = 3$$
$$-22y = 3 - 42$$
$$-22y = -39$$
$$y = \frac{39}{22}$$

Step4: Calculate $x$ value

Substitute $y = \frac{39}{22}$ into $x = 14 - 4y$:
$$x = 14 - 4\times\frac{39}{22} = 14 - \frac{78}{11} = \frac{154 - 78}{11} = \frac{76}{11}$$

Answer:

one solution