Question

Use the substitution method to solve the system of equations.choose the correct ordered pair. 3x+y=10

y=x-2

Answer 1

Answer: x= 3 and y=1

Explanation:

3x + y = 10 ------(1)

y = x - 2 ---------(2)

substitute equation(2) in equation (1)

3x + x - 2 =10

4x - 2 = 10

add 2 to bothside

4x - 2 +2 = 10+2

4x = 12

Divide bothside by 4

4x/4 = 12/4

x = 3

substitute x=3 in equation (1)

3x + y = 10

3(3) + y = 10

9 + y = 10

subtract y from bothside

9 + y - 9 = 10-9

y = 1

Therefore; x =3 and y=1

Answer 2

Given the system of equations:

`3x+y = 10` ...... (1)

`y=x-2` ......(2)

Substitute the equation (2) into (1);

`3x+x-2= 10`

Combine like terms;

4x-2 = 10

Add 2 to both sides we have;

4x= 12

Divide both sides by 4;

x = 3

Substitute in (2) to solve for y;

`y=3-2=1`

⇒y = 1

Therefore, the ordered pair is, (3, 1).