Question

What is the solution to the system of equations.x - 5y = 22x + y = 4

Answer 1

To answer this question, we can use the substitution method or the elimination method.

If we use the substitution method, we can proceed as follows:

1. Solve the first equation for x:

`x-5y=2`

If we add 5y to both sides of the equation, we have:

`x-5y+5y=2+5y\Rightarrow x=2+5y`

2. We can substitute the corresponding value of x - as a function of y - as follows:

`2(2+5y)+y=4`

3. Now, we can solve the equation for y as follows:

a. Apply the distributive property:

`2\cdot2+2\cdot5y+y=4\Rightarrow4+10y+y=4`

b. Adding like terms, and subtracting 4 from both sides:

`4+11y=4\Rightarrow4-4+11y=4-4\Rightarrow11y=0\Rightarrow y=0`

4. If we substitute this value for y in the first equation, we will have:

`x-5(0)=2\Rightarrow x=2`

Therefore, we have that the solution for this system of linear equations is x = 2, and y = 0.

We can check these results, if we substitute those values into the original equations:

x = 2

y = 0

`2-5(0)=2\Rightarrow2=2`
`2(2)+0=4\Rightarrow4=4`

In summary, we have that the solution to the system of equations is:

x = 2 and y = 0.