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
To solve this system of linear equations by graphing, we first need to rewrite each equation in slope-intercept form (y = mx + b).
1) Equation 1: y = x + 3
This equation is already in slope-intercept form. The slope is 1, and the y-intercept is 3.
2) Equation 2: -4x + 4y = 28
First, we rewrite this equation in slope-intercept form:
4y = 4x + 28
y = x + 7
The slope is 1, and the y-intercept is 7.
Now, we can graph both equations on the same set of axes. The first equation y = x + 3 has a y-intercept at (0,3) and a slope of 1, meaning it goes up one unit for every one unit to the right.
The second equation y = x + 7 has a y-intercept at (0,7) and also has a slope of 1.
When graphed, the two lines intersect at the point (4, 7), which means that this is the solution to the system of linear equations. This point represents the values of x and y that satisfy both equations simultaneously.
Therefore, the solution to the system of linear equations is x = 4 and y = 7.