Question

At what value of x do the graphs of the equations below intersect?

2x – y = 6

5x + 10y = –10

Answer 1

Explanation:

The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:

2x - y = 6

y = 2x - 6

We substitute the equation above to the second equation.

5x + 10y = –10

5x + 10( 2x - 6 )= –10

Simplifying,

5x + 20x - 60 = -10

25x = 50

x = 2

Therefore, the intersection has the value of x equal to 2.

Answer 2

Answer with Step-by-step explanation:

The point of intersection of the graphs of system of equation is the solution to the system of equations.

So, we need to find the solution of the system of equations:

2x – y = 6

5x + 10y = –10

Multiplying first equation by 10 and add it to second equation.

5x+10y+10(2x-y)= -10+60

5x+10y+20x-10y=50

25x=50

⇒ x=2

Hence, value of x where the graphs of the equations

2x – y = 6

5x + 10y = –10 intersect is:

x=2