At what value of x do the graphs of the equations below intersect? 2x − y = 6 5x + 10y = −10 −2 2

At x = -2, the graphs of equations 2x - y = 6 and 5x + 10y = -10 intersect at the point (-2,-2).

What is a graph?

A graph is a visual representation that shows the relationships between two or more items or values. It typically involves plotting points and connecting them to form a diagram.

To find the point of intersection of the graphs of equations 2x - y = 6 (i) and 5x + 10y = -10  (ii), we can follow these steps:

List out the points that satisfy each equation:

For equation (i):

• When x=6, we have 2(6) - y = 6, which gives us y = 6. So point (6,6) lies on the graph of equation (i).

• When x=0, we have 2(0) - y = 6, which gives us y = -6. So the point (0,-6) lies on the graph of equation (i).

• When x=3, we have 2(3) - y = 6, which gives us y = 0. So point (3,0) lies on the graph of equation (i).

For equation (ii):

• When x=0, we have 5(0) + 10y = -10, which gives us y = -1. So the point (0,-1) lies on the graph of equation (ii).

• When x=2, we have 5(2) + 10y = -10, which gives us y = 0. So point (2,0) lies on the graph of equation (ii).

• When x=4, we have 5(4) + 10y = -10, which gives us y = 1. So point (4,1) lies on the graph of equation (ii).

Plot the points on a graph and join them to get the graph of each equation.

Identify the point(s) of the intersection of the two graphs. From the graph, we see that the two graphs intersect at the point (-2,-2).

Therefore, we can conclude that at x = -2, the graphs of equations 2x - y = 6 and 5x + 10y = -10 intersect at the point (-2,-2).

Learn more about intersecting points of graphs here:

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Answer:

The solution to the equation is: (x,y) = (2,-2) If that helps

Step-by-step explanation:

// Solve equation [1] for the variable  y  

 [1]    y = 2x - 6

// Plug this in for variable  y  in equation [2]

  [2]    5x + 10•(2x-6) = -10

  [2]    25x = 50

// Solve equation [2] for the variable  x  

  [2]    25x = 50  

  [2]    x = 2  

// By now we know this much :

   x = 2

   y = 2x-6

// Use the  x  value to solve for  y  

   y = 2(2)-6 = -2  

Solution :

{x,y} = {2,-2}