Question

determine whether each ordered pair is a solution to the following system of equations.
y = 4x + 5
y = 3x + 3
(1,9) select 1
(3,12) select 1
(0,0) select 1
(-2,-3) select 1

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the system of equations, we substitute the \(x\) and \(y\) values into both equations and check if both equations are satisfied.

For \((1, 9)\):

Step 1: Substitute into \(y = 4x + 5\)

Substitute \(x = 1\) and \(y = 9\) into \(y = 4x + 5\):
\(9 = 4(1) + 5\)
\(9 = 4 + 5\)
\(9 = 9\) (True)

Step 2: Substitute into \(y = 3x + 3\)

Substitute \(x = 1\) and \(y = 9\) into \(y = 3x + 3\):
\(9 = 3(1) + 3\)
\(9 = 3 + 3\)
\(9 = 6\) (False)

Since it does not satisfy the second equation, \((1, 9)\) is not a solution.

For \((3, 12)\):

Step 1: Substitute into \(y = 4x + 5\)

Substitute \(x = 3\) and \(y = 12\) into \(y = 4x + 5\):
\(12 = 4(3) + 5\)
\(12 = 12 + 5\)
\(12 = 17\) (False)

Since it does not satisfy the first equation, \((3, 12)\) is not a solution.

For \((0, 0)\):

Step 1: Substitute into \(y = 4x + 5\)

Substitute \(x = 0\) and \(y = 0\) into \(y = 4x + 5\):
\(0 = 4(0) + 5\)
\(0 = 0 + 5\)
\(0 = 5\) (False)

Since it does not satisfy the first equation, \((0, 0)\) is not a solution.

For \((-2, -3)\):

Step 1: Substitute into \(y = 4x + 5\)

Substitute \(x = -2\) and \(y = -3\) into \(y = 4x + 5\):
\(-3 = 4(-2) + 5\)
\(-3 = -8 + 5\)
\(-3 = -3\) (True)

Step 2: Substitute into \(y = 3x + 3\)

Substitute \(x = -2\) and \(y = -3\) into \(y = 3x + 3\):
\(-3 = 3(-2) + 3\)
\(-3 = -6 + 3\)
\(-3 = -3\) (True)

Since it satisfies both equations, \((-2, -3)\) is a solution.

Answer:

• \((1, 9)\): Not a solution
• \((3, 12)\): Not a solution
• \((0, 0)\): Not a solution
• \((-2, -3)\): Solution