Review the graphs of a system of two linear equations in two

variables: x - 5y = 7 and
3х - 2y = -4. Find the solution to both equations.
(1 point)
The intersection point is
Explain

1 answer

To review the graphs of the system of linear equations, let's start by rearranging both equations to slope-intercept form (y = mx + b):

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

2) 3x - 2y = -4
-2y = -3x - 4
y = (3/2)x + 2

Now, we can see that the slopes of the two lines are different. The slope of the first equation (1/5) is smaller than the slope of the second equation (3/2). Therefore, the lines will intersect at a single point.

To find the intersection point, we can set the two equations equal to each other:

(1/5)x - 7/5 = (3/2)x + 2

Let's solve for x:

Multiply through by 10 to get rid of the fractions:

2x - 14 = 15x + 20

Combine like terms:

2x - 15x = 20 + 14
-13x = 34

Divide by -13:

x = -34/13

Now substitute this value of x back into either equation to solve for y. Let's use the first equation:

y = (1/5)(-34/13) - 7/5

Simplify:

y = -34/65 - 91/65
y = -125/65

Therefore, the solution to the system of equations is x = -34/13 and y = -125/65 (-2.62, -1.92 rounded to two decimal places).

The intersection point is where the two lines cross, and in this case, it is approximately (-2.62, -1.92).