Question

for each ordered pair, determine whether it is a solution to $7x - 4y = -5$.

$(x, y)$	is it a solution? - yes	is it a solution? - no
$(-3, -4)$	$circ$	$circ$
$(-2, 6)$	$circ$	$circ$
$(5, 1)$	$circ$	$circ$

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the equation \(7x - 4y = -5\), 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 \(-5\)).

For the ordered pair \((4, 2)\)

Step 1: Substitute \(x = 4\) and \(y = 2\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x = 4\) and \(y = 2\), we get:
\(7\times4-4\times2\)
First, calculate the multiplications: \(7\times4 = 28\) and \(4\times2=8\)
Then, perform the subtraction: \(28 - 8=20\)
Since \(20
eq - 5\), the ordered pair \((4, 2)\) is not a solution.

For the ordered pair \((-3,-4)\)

Step 1: Substitute \(x=-3\) and \(y = - 4\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x=-3\) and \(y=-4\), we get:
\(7\times(-3)-4\times(-4)\)
First, calculate the multiplications: \(7\times(-3)=-21\) and \(4\times(-4)=-16\), so \(-4\times(-4) = 16\)
Then, perform the addition (because \(-21+16\)): \(-21 + 16=-5\)
Since \(-5=-5\), the ordered pair \((-3,-4)\) is a solution.

For the ordered pair \((-2,6)\)

Step 1: Substitute \(x = - 2\) and \(y = 6\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x=-2\) and \(y = 6\), we get:
\(7\times(-2)-4\times6\)
First, calculate the multiplications: \(7\times(-2)=-14\) and \(4\times6 = 24\)
Then, perform the subtraction: \(-14-24=-38\)
Since \(-38
eq - 5\), the ordered pair \((-2,6)\) is not a solution.

For the ordered pair \((5,1)\)

Step 1: Substitute \(x = 5\) and \(y = 1\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x = 5\) and \(y = 1\), we get:
\(7\times5-4\times1\)
First, calculate the multiplications: \(7\times5 = 35\) and \(4\times1=4\)
Then, perform the subtraction: \(35 - 4 = 31\)
Since \(31
eq - 5\), the ordered pair \((5,1)\) is not a solution.

Final Answers for each ordered pair:

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

Answer:

To determine if an ordered pair \((x, y)\) is a solution to the equation \(7x - 4y = -5\), 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 \(-5\)).

For the ordered pair \((4, 2)\)

Step 1: Substitute \(x = 4\) and \(y = 2\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x = 4\) and \(y = 2\), we get:
\(7\times4-4\times2\)
First, calculate the multiplications: \(7\times4 = 28\) and \(4\times2=8\)
Then, perform the subtraction: \(28 - 8=20\)
Since \(20
eq - 5\), the ordered pair \((4, 2)\) is not a solution.

For the ordered pair \((-3,-4)\)

Step 1: Substitute \(x=-3\) and \(y = - 4\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x=-3\) and \(y=-4\), we get:
\(7\times(-3)-4\times(-4)\)
First, calculate the multiplications: \(7\times(-3)=-21\) and \(4\times(-4)=-16\), so \(-4\times(-4) = 16\)
Then, perform the addition (because \(-21+16\)): \(-21 + 16=-5\)
Since \(-5=-5\), the ordered pair \((-3,-4)\) is a solution.

For the ordered pair \((-2,6)\)

Step 1: Substitute \(x = - 2\) and \(y = 6\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x=-2\) and \(y = 6\), we get:
\(7\times(-2)-4\times6\)
First, calculate the multiplications: \(7\times(-2)=-14\) and \(4\times6 = 24\)
Then, perform the subtraction: \(-14-24=-38\)
Since \(-38
eq - 5\), the ordered pair \((-2,6)\) is not a solution.

For the ordered pair \((5,1)\)

Step 1: Substitute \(x = 5\) and \(y = 1\) into the left - hand side of the equation

The left - hand side of the equation is \(7x-4y\). Substituting \(x = 5\) and \(y = 1\), we get:
\(7\times5-4\times1\)
First, calculate the multiplications: \(7\times5 = 35\) and \(4\times1=4\)
Then, perform the subtraction: \(35 - 4 = 31\)
Since \(31
eq - 5\), the ordered pair \((5,1)\) is not a solution.

Final Answers for each ordered pair:

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