Question

Use the substitution method to solve the system of equations. Choose the

correct ordered pair.
x+ 3y = 10
y= x + 2
A. (-2,4)
B. (1,3)
C. (7,1)
D. (2,4)

Answer 1

B. (1 , 3 )

Explanation:

Step 1 Rearrange.

`x + 3y = 10 \: \: (1) \\ y = x + 2 \: \: \: (2) \\ x + 3y = 10 \: \: (1)\\ x - y = - 2 \: \: \: (2)\\`

Step 2 : Multiply equation 1 by the coefficient of x in equation 2

Step 2 : Multiply equation 1 by the coefficient of x in equation 2Multiply equation 2 by the coefficient of x in equation 1

Step 3 : Subtract equation 4 from equation 3 and solve for y

`x + 3y = 10 \: \: (3)\\ x - y = - 2 \: \: \: (4) \\ 4y = 12 \\ (4y)/(4) = (12)/(4) \\`

Substitute the value for y in to equation 1. or equation 2 and solve for x .

`y = 3 \\substitute \: 3 \: for \: y \: \\ in \: eq \: 1 \: or \: 2 \\ x + 3y = 10 \\ x + 3(3) = 10`

`x + 9 = 10 \\ x = 10 - 9 \\ x = 1 \\ \\ (x \: y) = (1 \: \: 3)`