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Math  /  Algebra

QuestionQuestion 2 of 10 Use the substitution method to solve the system of equations. Choose the correct ordered pair. x+2y=12y=x+3\begin{array}{l} x+2 y=12 \\ y=x+3 \end{array} A. (2,1)(2,1) B. (2,5)(2,5) C. (5,8)(5,8) D. (5,2)(5,2) SUBmit

Studdy Solution

STEP 1

1. We are given a system of two equations with two variables.
2. The substitution method involves solving one equation for one variable and substituting that expression into the other equation.
3. The goal is to find the ordered pair (x,y)(x, y) that satisfies both equations.

STEP 2

1. Solve one of the equations for one variable.
2. Substitute the expression from Step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute back to find the other variable.
5. Check which ordered pair is correct.

STEP 3

We are given the equations:
x+2y=12 x + 2y = 12 y=x+3 y = x + 3
The second equation is already solved for y y . We will use this equation for substitution.

STEP 4

Substitute y=x+3 y = x + 3 into the first equation x+2y=12 x + 2y = 12 :
x+2(x+3)=12 x + 2(x + 3) = 12

STEP 5

Simplify the equation:
x+2x+6=12 x + 2x + 6 = 12
Combine like terms:
3x+6=12 3x + 6 = 12

STEP 6

Solve for x x by isolating it:
Subtract 6 from both sides:
3x=6 3x = 6
Divide both sides by 3:
x=2 x = 2

STEP 7

Substitute x=2 x = 2 back into the equation y=x+3 y = x + 3 :
y=2+3 y = 2 + 3
y=5 y = 5

STEP 8

The solution to the system of equations is the ordered pair (x,y)=(2,5)(x, y) = (2, 5).
Check which option matches:
A. (2,1)(2, 1) B. (2,5)(2, 5) C. (5,8)(5, 8) D. (5,2)(5, 2)
The correct answer is B. (2,5)(2, 5).

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