Question

Solve the following system of equations by using the substitution method. y = x + 3 and y = 2x – 4

Answer 1

x=7 and y=10

Explanation:

y=x+3 ......eqn (1)

y=2x-4 .......eqn(2)

From equation 1

x=y-3 .......eqn (3)

Subtitude equation 3 into equation 2

y=2(y-3)-4

y=2y-6-4

y=2y-10

y-2y=-10

-y=-10

y=10

Subtitude y=10 into equation 3

x=10-3

x=7

Answer 2

x=7, y=10

Explanation:

Given equation set is :

`\[y = x + 3\]` ---------------(1)

`\[y = 2x - 4\]` ---------------(2)

Simplifying (1) to express x in terms of y:

`\[x = y - 3\]` ---------------- (3)

Substituting this value of x in (2) and solving:

`\[y = 2*(y-3) - 4\]`

=>
`\[y = 2y - 6 - 4\]`

=>
`\[y = 2y - 10\]`

=>
`\[2y - y = 10\]`

=>
`\[y = 10\]`

Substituting this value of y in (3) :

`\[x = 10 - 3\]`

=>
`\[x = 7\]`

So the required solution is x=7,y=10.