Question

Solve the following system of linear equations by graphing.
y=x+3

−4x+4y=28

Answer 1

To solve the system of equations by graphing, we first need to express each equation in slope-intercept form (y = mx + b) if they are not already in that form.

### First Equation:
The first equation is already in slope-intercept form:
\[ y = x + 3 \]

### Second Equation:
The second equation is:
\[ -4x + 4y = 28 \]

We can solve for \(y\):
1. Add \(4x\) to both sides:
\[ 4y = 4x + 28 \]
2. Divide each term by \(4\):
\[ y = x + 7 \]

### Now we have the two equations:
1. \( y = x + 3 \)
2. \( y = x + 7 \)

### Graphing the Equations:
1. **For the first equation \( y = x + 3 \)**:
- When \(x = 0\), \(y = 3\) (point: (0, 3))
- When \(x = -3\), \(y = 0\) (point: (-3, 0))
- When \(x = 3\), \(y = 6\) (point: (3, 6))

2. **For the second equation \( y = x + 7 \)**:
- When \(x = 0\), \(y = 7\) (point: (0, 7))
- When \(x = -4\), \(y = 3\) (point: (-4, 3))
- When \(x = 3\), \(y = 10\) (point: (3, 10))

### Plotting:
- Plot the points for both lines on a graph.
- Draw a line through the points for each equation.

### Conclusion:
From the equations \(y = x + 3\) and \(y = x + 7\), we see that both lines are parallel (they have the same slope of 1) but different y-intercepts (3 and 7).

### Result:
Since the lines do not intersect, there is no solution to this system of equations. The system is inconsistent.