Question

Find the solution to the system of equations by using the substitution method

Y=4x+1
Y=x+1

Answer 1

x = 0

y = 1

Explanation:

y = 4x + 1 -------eqn 1

y = x + 1 -------eqn 2

Looking for x, let's use eqn 1

y = 4x + 1

4x = y - 1

Divide both sides by 4, to get x

4x/4 = (y - 1) / 4

x = (y - 1) / 4

Substitute the value of x into eqn 2

y = x + 1

y = (y - 1) / 4 + 1

LCM = 4

y =( y - 1 + 4)/4

y =( y + 3) / 4

Cross multiply

y * 4 = y + 3

4y = y + 3

4y - y = 3

3y = 3

Divide both sides by 3, to get y

3y / 3 = 3/3

y = 1

Substitute y = 1 , into eqn 1

y = 4x + 1

1 = 4x + 1

1 -1 = 4x

0 = 4x

Divide both sides by 4, to get x

0/4 = 4x/4

0 = x

x = 0

Hint, let's check if the values are correct

Let's pick eqn 2

y = x + 1

y = 1

x = 0

1 = 0 + 1

1 = 1

Correct

Let's try the eqn 1

y = 4x + 1

1 = 4(0) + 1

1 = 0 + 1

1 = 1

Correct too