Review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 3y + 4= Find the surullion to both equations

Answer 1

To analyze the graphs of the system of two linear equations, we first need to put them in slope-intercept form, which is y = mx + b.

For the first equation, x - 5y = 7, we can isolate y by subtracting x from both sides:

-5y = -x + 7.

Next, we divide both sides by -5:

y = (1/5)x - 7/5.

So, the slope of the first equation is 1/5 and the y-intercept is -7/5.

For the second equation, 3x - 3y + 4 = 0, we isolate y by subtracting 3x and 4 from both sides:

-3y = -3x - 4.

Next, we divide both sides by -3:

y = x + 4/3.

So, the slope of the second equation is 1 and the y-intercept is 4/3.

Now we can graph these equations:

The graph of y = (1/5)x - 7/5 represents a line with a positive slope of 1/5. It intersects the y-axis at -7/5, which is a little below y = -1. The line is increasing as x increases, with a steepness of 1 unit vertically for every 5 units horizontally.

The graph of y = x + 4/3 represents a line with a slope of 1. It intersects the y-axis at 4/3, which is slightly above y = 1. The line is increasing as x increases, with a steepness of 1 unit vertically for every 1 unit horizontally.

To find the solution to both equations, we need to find the point where the two graphs intersect. From the graphs, it is clear that the lines intersect at the point (1, 9/3) or (1, 3).

Therefore, the solution to the system of equations is x = 1 and y = 3.