Question

Tina wrote the equations 3x - y = 9 and 4x + y + 5, What can Tina conclude about the solution to this system of equations?

a. (–3, 2) is a solution to the system of linear equations.
b. (–2, 3) is a solution to the system of linear equations.
c. (2, –3) is a solution to the system of linear equations.
d. (3, –2) is a solution to the system of linear equations.

Answer 1

3x - y = 9
4x + y = 5
---------------add
7x = 14
x = 14/7
x = 2

3x - y = 9
3(2) - y = 9
6 - y = 9
-y = 9 - 6
-y = 3
y = -3

C. (2,-3) is a solution to the system of linear equations

Answer 2

C. (2, –3) is a solution to the system of linear equations.

Explanation:

Given equations are,

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14 ( Combine like terms )

x = 2 ( Divide both sides by 7 ),

From equation (1),

3(2) - y = 9

6 - y = 9

-y = 9 - 6 ( Subtraction 6 on both sides )

-y = 3

⇒ y = - 3 ( Multiplying -1 on both sides )

Hence, the solution of the system of equations is (2,-3),

Option 'C' is correct.