Use the image to answer the question. Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4 . Find the solution to both equations. (1 point) The intersection point is ().
The intersection point of two linear equations in two variables represents the solution to the system of equations. To find the intersection point, we can solve the system using either substitution or elimination method.
Let's solve it using the elimination method:
We have the system of equations:
x - 5y = 7 ...(1)
3x - 2y = -4 ...(2)
We can multiply equation (1) by 3 and equation (2) by 1 to make the coefficients of x in each equation equal:
3(x - 5y) = 3(7)
1(3x - 2y) = 1(-4)
Simplifying these equations, we get:
3x - 15y = 21 ...(3)
3x - 2y = -4 ...(4)
Now, subtract equation (4) from equation (3):
(3x - 15y) - (3x - 2y) = 21 - (-4)
3x - 15y - 3x + 2y = 21 + 4
-13y = 25
Dividing by -13 on both sides, we get:
y = -25/13
Now substitute this value of y into equation (1):
x - 5(-25/13) = 7
x + 125/13 = 7
x = 7 - 125/13
x = (91-125)/13
x = -34/13
Therefore, the intersection point is (-34/13, -25/13).
To find the intersection point of the two equations, we need to solve the system of equations. From the given equations:
Equation 1: x−5y=7
Equation 2: 3x−2y=−4
We can solve this system of equations using various methods such as substitution, elimination, or graphing. However, since you mentioned that there is an image available, let's assume that the image shows the graph of the equations.
Looking at the graph, the intersection point is the point where the two lines intersect.
Unfortunately, as an AI text-based assistant, I am unable to see or interpret images. Please provide the graph or any additional information associated with the image, and I'll be happy to assist you further in finding the solution.
To find the solution to a system of linear equations graphically, you need to find the point at which the graphs of the equations intersect.
Looking at the given equations, we have x - 5y = 7 and 3x - 2y = -4.
To find the intersection point, we can use a graphing tool or draw the graphs of the equations manually. However, since the image is not provided, I cannot analyze it and determine the intersection point for you.
Here's how you can find the intersection point on your own:
1. Solve the first equation for x: x = 7 + 5y.
2. Substitute the value of x from step 1 into the second equation: 3(7 + 5y) - 2y = -4.
3. Simplify the equation from step 2 to find the value of y.
4. Substitute the value of y obtained from step 3 back into either equation to find the corresponding value of x.
5. The solution to the system of equations is the point (x, y) obtained from step 4.
Please provide the image depicting the graphs of the two equations, and I will be happy to assist further in finding the solution.