To solve the system of equations and describe the graph, let's start with the given equations:
1. \( y = x + 3 \)
2. \( -4x + 4y = 28 \)
First, let's rewrite the second equation in a simpler form. We can divide the entire equation by 4:
\[ -x + y = 7 \]
Now we have the system of equations:
1. \( y = x + 3 \)
2. \( -x + y = 7 \)
Since the first equation is already solved for \( y \), we can substitute \( y = x + 3 \) into the second equation:
\[ -x + (x + 3) = 7 \]
Simplify the equation:
\[ -x + x + 3 = 7 \]
\[ 3 = 7 \]
Clearly, this is a contradiction. The conclusion is that there are no solutions to this system, which implies that the lines are parallel and never intersect.
### Graph Description
To describe the graph, we should consider the slope and intercepts of each line.
**First Equation: \( y = x + 3 \)**
- This is a linear equation in slope-intercept form \( y = mx + b \), where \( m = 1 \) and \( b = 3 \).
- The slope \( m \) is 1, meaning the line rises 1 unit for every unit it moves to the right.
- The y-intercept \( b \) is 3, meaning the line crosses the y-axis at \( (0, 3) \).
**Second Equation: \( -x + y = 7 \)**
- This can also be rewritten in slope-intercept form as \( y = x + 7 \) (add \( x \) to both sides).
- The slope \( m \) is again 1.
- The y-intercept is now 7, meaning the line crosses the y-axis at \( (0, 7) \).
**Graphing Both Lines**
- Both lines have the same slope (1), making them parallel to each other.
- They have different y-intercepts, 3 and 7, so they never intersect.
In conclusion, the graph consists of two parallel lines:
- One line passes through the point (0, 3) and goes up at a 45-degree angle.
- The other line passes through the point (0, 7) and goes up at the same 45-degree angle.
Since the lines are parallel and do not intersect, there is no solution to the system of equations.
Solve y=x+3,-4x+4y=28 describe what the graph would look like
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