Question

Y = x - 2 and y=-2x +7

Answer 1

x = 3 , y = 1

Explanation:

Solve the following system:

{y = x - 2 | (equation 1)

y = 7 - 2 x | (equation 2)

Express the system in standard form:

{-x + y = -2 | (equation 1)

2 x + y = 7 | (equation 2)

Swap equation 1 with equation 2:

{2 x + y = 7 | (equation 1)

-x + y = -2 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{2 x + y = 7 | (equation 1)

0 x+(3 y)/2 = 3/2 | (equation 2)

Multiply equation 2 by 2/3:

{2 x + y = 7 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{2 x+0 y = 6 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 3 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = 3 , y = 1

Answer 2

`\huge\boxed{\boxed{\bold{(3, 1)}}}`

`\hrulefill`

I'm assuming you need to find the solution to this system of equations (where the lines intersect).

We can use the substitution method to solve this system. Take the value of
`y` from the second equation and substitute it into the first:

`-2x+7=x-2`

Add
`2x` to both sides of the new equation:

`7=3x-2`

Now add
`2` to both sides of the equation:

`9=3x`

Divide both sides by
`3`:

`\boxed{3}=x`

Now let's solve for
`y` by substituting the known value of
`x` into the first equation:

`y=3-2`

Simplify using subtraction:

`y=\boxed{1}`

This means our solution is:

`\large\boxed{(3, 1)}`