Question

for each ordered pair, determine whether it is a solution to $7x + 4y = -23$.

$(x, y)$	is it a solution?
$(-1, -4)$	$\circ$	$\circ$
$(-5, 3)$	$\circ$	$\circ$
$(6, -7)$	$\circ$	$\circ$
$(2, 6)$	$\circ$	$\circ$

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the equation \(7x + 4y=-23\), we substitute the values of \(x\) and \(y\) into the equation and check if the left - hand side (LHS) equals the right - hand side (RHS, which is \(-23\)).

Step 1: Check the ordered pair \((-1,-4)\)

Substitute \(x = - 1\) and \(y=-4\) into the left - hand side of the equation \(7x + 4y\):

$$
LATEXBLOCK0
$$

Since \(LHS = RHS=-23\), \((-1,-4)\) is a solution.

Step 2: Check the ordered pair \((-5,3)\)

Substitute \(x = - 5\) and \(y = 3\) into the left - hand side of the equation \(7x+4y\):

$$
LATEXBLOCK1
$$

Since \(LHS=RHS = - 23\), \((-5,3)\) is a solution.

Step 3: Check the ordered pair \((6,-7)\)

Substitute \(x = 6\) and \(y=-7\) into the left - hand side of the equation \(7x + 4y\):

$$
LATEXBLOCK2
$$

Since \(14
eq - 23\), \((6,-7)\) is not a solution.

Step 4: Check the ordered pair \((2,6)\)

Substitute \(x = 2\) and \(y = 6\) into the left - hand side of the equation \(7x+4y\):

$$
LATEXBLOCK3
$$

Since \(38
eq-23\), \((2,6)\) is not a solution.

Answer:

• For \((-1,-4)\): Yes
• For \((-5,3)\): Yes
• For \((6,-7)\): No
• For \((2,6)\): No