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) simple steps
To solve the system of linear equations by graphing, we need to graph each equation and find the point where they intersect.
To graph the first equation, y = x + 3, we can start by finding its y-intercept, which is 3. This means that the line passes through the point (0, 3). We can also find another point by choosing any x-value and plugging it into the equation. Let's choose x = 1. We get y = 1 + 3 = 4, so another point on the line is (1, 4).
To graph the second equation, -4x + 4y = 28, we can rewrite it in slope-intercept form by isolating y. Subtracting -4x from both sides gives 4y = 4x + 28, and dividing by 4 gives y = x + 7. The y-intercept is 7, so the line passes through the point (0, 7). Using another point, let's choose x = 1 again. Plugging it into the equation, we get y = 1 + 7 = 8, so another point on the line is (1, 8).
Now we can plot these points on a graph and draw the lines that connect them. The first equation, y = x + 3, is a diagonal line with a positive slope of 1, meaning it rises as it moves to the right. The second equation, y = x + 7, is also a diagonal line with a positive slope of 1, but it starts at a higher y-value than the first line.
When we graph these lines, we can see that they intersect at the point (5, 8). This means that (5, 8) is the solution to the system of linear equations.
The graph visually represents the solution to the system. Since the two lines intersect at a single point, it tells us that there is exactly one solution to the system.