Select the statement that correctly describes the solution to this system of equations.
5x + 10y = 5
4x + 8y = 5
There is no solution
There is exactly one solution at (5,5)
There are infinitely many solutions
There is exactly one solution at (1,0)

Respuesta :

Answer:

No solution

If you multiply the 1st by 4 and the second by -5

The result is

20x +40y= 20

-20x-40y= -20

When you add both equations the result is  0=0

Step-by-step explanation:

There is no solution for 5x + 10y = 5; 4x + 8y = 5 as they are parallel lines.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The given pair of equation is :

5x + 10y = 5

4x + 8y = 5

[tex]a_1[/tex] =5, [tex]b_1[/tex]=10, [tex]c_1[/tex]=5

[tex]a_2[/tex]= 4, [tex]b_2[/tex]= 8, [tex]c_2[/tex]= 5

Now, checking the different condition on two pair of equations

So, we have the satisfied condition as

[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

= [tex]\frac{5}{4} =\frac{10}{8}\neq \frac{5}{5}[/tex]

which is condition for parallel.

Thus, There is no solution

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