Question

Solve the system of equations by using the substitution method.
3x-5y=14
y=x-4

Answer 1

The system would equate to (3,-1). X=3 and y=-1

Substitute is plugging in one value into another equation to solve it. In this system of equations, the value of y is given which can be plugging in to 3x-5y=14.

First plug the value of y in to the equation which will give you 3x-5(x-4)=14. Next you want to distribute -5 to the terms in the parentheses which will leave you with 3x-5x+20=14. Afterwards you want to add like terms and get -2x+20=14. Subtract on both sides by 20 and get -2x=-6, isolate x by dividing by -2 on both sides. X=3.

Now that you have the value of x you need to find the value of y. Plug x into y=x-4 so that you get y=3-4 which will give you y=-1.

Answer 2

x = 3

y = -1

(3, -1)

Explanation:

Substitute the y variable in 3x-5y=14 with the expression x-4

3x - 5y = 14

3x - 5(x - 4) = 14 Use the distributive property

3x - (5x - 20) = 14 Subtract the binomial

3x - 5x + 20 = 14 Collect like terms

20 - 2x = 14 Isolate "x" now

-2x = 14 - 20 Subtract 20 from both sides

-2x = -6 Divide both sides by -2

x = 3 Solved for x

Substitute x using 3 in one of the equations.

y = x - 4

y = 3 - 4 Subtract

y = -1 Solved for y

The solution as an ordered pair (x, y) is (3, -1).