Answered

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How many solutions does this system of equations have?

[tex]\[
\begin{array}{l}
y = 4x + 4 \\
y = 4x - 1
\end{array}
\][/tex]

A. Two solutions
B. One solution
C. No solution
D. Infinite solutions

Sagot :

GinnyAnswer
To determine how many solutions a given system of linear equations has, we follow these steps:

### System of Equations
Given the equations:
1. \( y = 4x + 4 \)
2. \( y = 4x - 1 \)

### Analyzing the Equations
1. Compare the slopes: Notice that both equations are written in the slope-intercept form \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept.
- For \( y = 4x + 4 \), the slope (\( m \)) is 4.
- For \( y = 4x - 1 \), the slope (\( m \)) is also 4.

2. Compare the y-intercepts:
- In \( y = 4x + 4 \), the y-intercept is 4.
- In \( y = 4x - 1 \), the y-intercept is -1.

### Conclusion
- The slopes of the two lines are equal, which means the lines are parallel.
- Their y-intercepts are different, which means they do not coincide.

Since parallel lines that do not coincide will never intersect, this system of equations has:

No solution.
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