Question

Use substitution to solve the system. 5X+3Y=22 Y=2X-11

Answer 1

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.

We can solve this problem in two steps, Comprehending, and Solving/Checking our answers. I'll be starting off with Comprehending.

Comprehending

We can solve the problem with substitution by finding out what one variable is equal to in terms of the second variable.

This is what we would call System of Equations where we need to find the point where the lines hit.

We can do this either with Graphing, or Algebra. In this case, we need to use substitution, so it has to be Algebraically.

Now that we know how to solve it/what to do, we can start solving.

Solving

We can solve the problem by first replacing y with its correct value in terms of x. Since we know the two equations, we can begin solving.

$y=2x-11\\5x+3y=22$

We can solve it by inserting our y value into the y value of the second equation.

$5x+3(2x-11)=22\\5x+6x-33=22\\11x=22+33\\11x=55\\x=5$

Now that we know our x value, we can solve for y by inserting it into an equation.

$y=2(5)-11\\y=10-11\\y=-1$

Now that we have solved, we have gotten out point of (5,-1)

We can test this by inputting it into an equation. (Any of the latter).

$5(5)+3(-1)=22?\\25-3=22?\\22=22$

Now that we have checked our answer and it appears correct, we have gotten our answer of (5,-1).

Answer 2

Answer:

(5, - 1 )

Step-by-step explanation:

5x + 3y = 22 → (1)

y = 2x - 11 → (2)

Substitute y = 2x - 11 into (1)

5x + 3(2x - 11) = 22 ← distribute parenthesis and simplify left side

5x + 6x - 33 = 22

11x - 33 = 22 ( add 33 to both sides )

11x = 55 ( divide both sides by 11 )

x = 5

Substitute x = 5 into (2)

y = 2(5) - 11 = 10 - 11 = - 1

solution is (5, - 1 )