Question Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations. y=x+3 −4x+4y=28 (2 points)
To graph the system of linear equations, we need to find the points of intersection between the two lines represented by the equations.
First, we will graph the equation y = x + 3.
We can start by assigning values to x and solving for y to find points on the line.
When x = 0, y = 0 + 3 = 3. This gives us one point (0, 3) on the line.
When x = 1, y = 1 + 3 = 4. This gives us another point (1, 4) on the line.
We can continue this process and find more points. Alternatively, we can find two points and draw a straight line passing through them.
Next, we will graph the equation -4x + 4y = 28.
To graph this equation, we will first solve for y.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Again, we can assign values to x and solve for y to find points on the line.
When x = 0, y = 0 + 7 = 7. This gives us one point (0, 7) on the line.
When x = 1, y = 1 + 7 = 8. This gives us another point (1, 8) on the line.
We can continue this process and find more points or draw a straight line passing through the given points.
Now, we can graph the two lines on the same coordinate plane:
The line representing y = x + 3 passes through the points (0, 3) and (1, 4). It has a positive slope, meaning it slopes upwards from left to right.
The line representing y = x + 7 passes through the points (0, 7) and (1, 8). It also has a positive slope.
The two lines intersect at the point (4, 7).
This intersection point is the solution to the system of linear equations. Hence, the solution to the system of linear equations is x = 4 and y = 7.
Graphically, the lines intersect at a single point, indicating that there is a unique solution to the system of linear equations.