Question

What is the solution to the system of equations: 4x-y=10 and x-4=y

Answer 1

x = 2 , y = -2

Explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

Answer 2

(2, - 2 )

Explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )