Question

Solve this system of equation using the substitution method

2x + y = 5

y = x - 4

Answer 1

`\boxed {\boxed {\sf (3, -1)}}`

Explanation:

We are asked to solve this system of equations using substitution:

`2x+y=5\\y=x-4`

Since y is equal to x-4, we can substitute x-4 in the top equation.

`2x+(x-4)=5`

`2x+x-4=5`

Combine the like terms on the left side of the equation. 2x and x both have the variable x and can be added.

`3x-4=5`

Now, solve for x by isolating the variable. 4 is being subtracted and the inverse of subtraction is addition. Add 4 to both sides.

`3x-4+4=5+4\\3x=5+4\\3x=9`

x is being multiplied by 3 and the inverse of multiplication is division. Divide both sides by 3.

`3x/3=9/3 \\x=9/3 \\x=3`

x is equal to 3. Substitute 3 back into the bottom equation to find y.

`y=x-4\\y=3-4\\y=-1`

Points are written as (x,y). The solution to this system of equations is (3, -1).