Find the solution to the system of equations by using the substitution method
Y=4x+1
Y=x+1

x = 0

y = 1

Step-by-step 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

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!