Question

Solve the system of equations by substitution,

y = 2x - 4
y = x + 1

a.(2,3)
b.(5,6)
c.(4,8)
d.(3,1)

Answer 1

The solution to the system of equations is:

(x, y) = (5, 6)

Hence, option B is correct.

Explanation:

Given the system of equations

y = 2x - 4

y = x + 1

Solving the system of equations by substitution method.

`\begin{bmatrix}y=2x-4\\ y=x+1\end{bmatrix}`

Substitute y = x+1 in y = 2x - 4

`x+1=2x-4`

Subtract 1 from both sides

`x+1-1=2x-4-1`

Simplify

`x=2x-5`

Subtract 2x from both sides

`x-2x=2x-5-2x`

Simplify

`-x=-5`

Divide both sides by -1

`(-x)/(-1)=(-5)/(-1)`

Simplify

`x=5`

For y = x+1

substitute x = 5

`y=5+1`

Simplify

`y = 6`

Therefore, the solution to the system of equations is:

(x, y) = (5, 6)

Hence, option B is correct.