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.

Question

(1 point)
The intersection point is ( ).

Answer 1

To find the solution to a system of linear equations, we need to find the point where the graphs of the equations intersect.

Let's first graph the equations:

For the equation x - 5y = 7:

We can rewrite this equation in slope-intercept form (y = mx + b) by isolating y:
-5y = -x + 7
y = (1/5)x - (7/5)

The graph of this equation is a line with a slope of 1/5 and a y-intercept of -7/5.

For the equation 3x - 2y = -4:

We can rewrite this equation in slope-intercept form (y = mx + b) by isolating y:
-2y = -3x - 4
y = (3/2)x + 2

The graph of this equation is a line with a slope of 3/2 and a y-intercept of 2.

Now, let's plot the graphs and find the intersection point.

The graphs intersect at the point (3, 1).

Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is x = 3 and y = 1.

Answer 2

The intersection point is ?

Answer 3

The intersection point is (3, 1).

Answer 4

are you sure?

Answer 5

I apologize for the incorrect response in my previous message. Upon closer examination, it appears that I made an error in my calculations.

Let's re-evaluate the solution.

To find the solution to the system of equations, we can solve them simultaneously by substitution or elimination method.

Given the equations:

1) x - 5y = 7
2) 3x - 2y = -4

Let's solve the system using the elimination method.

Multiplying equation 1) by 3, we get:
3x - 15y = 21

Now, we can subtract equation 2) from the modified equation 3x - 15y = 21:

(3x - 15y) - (3x - 2y) = 21 - (-4)
-13y = 25
y = 25 / -13
y ≈ -1.923

Now substitute the value of y into equation 1) to solve for x:

x - 5(-1.923) = 7
x + 9.615 = 7
x = 7 - 9.615
x ≈ -2.615

Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is approximately x ≈ -2.615 and y ≈ -1.923.