Question

this is the graph of the equation $3x + 7y = -12$.
which ordered pairs are solutions to the equation? select all that apply

Explanation:

Since the specific ordered pairs to check are not provided, we can use the following general method to determine if an ordered pair \((x,y)\) is a solution to the equation \(3x + 7y=-12\):

Step - by - Step Format:

Step 1: Substitute the \(x\) and \(y\) values of the ordered pair into the equation

For an ordered pair \((x_0,y_0)\), substitute \(x = x_0\) and \(y=y_0\) into the left - hand side of the equation \(3x + 7y\). The equation is \(3x+7y=-12\), so we calculate \(3x_0 + 7y_0\).

Step 2: Check if the result equals \(- 12\)

If \(3x_0+7y_0=-12\), then the ordered pair \((x_0,y_0)\) is a solution to the equation; otherwise, it is not.

For example, let's check the ordered pair \((- 4,0)\):

• Step 1: Substitute \(x=-4\) and \(y = 0\) into \(3x + 7y\). We get \(3\times(-4)+7\times0=-12 + 0=-12\).
• Step 2: Since \(-12=-12\), the ordered pair \((-4,0)\) is a solution.

Another example, check the ordered pair \((0,-\frac{12}{7})\):

• Step 1: Substitute \(x = 0\) and \(y=-\frac{12}{7}\) into \(3x + 7y\). We get \(3\times0+7\times(-\frac{12}{7})=0 - 12=-12\).
• Step 2: Since \(-12=-12\), the ordered pair \((0,-\frac{12}{7})\) is a solution.

If you provide the specific ordered pairs, we can check each of them one by one using the above method.

Answer:

Since the specific ordered pairs to check are not provided, we can use the following general method to determine if an ordered pair \((x,y)\) is a solution to the equation \(3x + 7y=-12\):

Step - by - Step Format:

Step 1: Substitute the \(x\) and \(y\) values of the ordered pair into the equation

For an ordered pair \((x_0,y_0)\), substitute \(x = x_0\) and \(y=y_0\) into the left - hand side of the equation \(3x + 7y\). The equation is \(3x+7y=-12\), so we calculate \(3x_0 + 7y_0\).

Step 2: Check if the result equals \(- 12\)

If \(3x_0+7y_0=-12\), then the ordered pair \((x_0,y_0)\) is a solution to the equation; otherwise, it is not.

For example, let's check the ordered pair \((- 4,0)\):

• Step 1: Substitute \(x=-4\) and \(y = 0\) into \(3x + 7y\). We get \(3\times(-4)+7\times0=-12 + 0=-12\).
• Step 2: Since \(-12=-12\), the ordered pair \((-4,0)\) is a solution.

Another example, check the ordered pair \((0,-\frac{12}{7})\):

• Step 1: Substitute \(x = 0\) and \(y=-\frac{12}{7}\) into \(3x + 7y\). We get \(3\times0+7\times(-\frac{12}{7})=0 - 12=-12\).
• Step 2: Since \(-12=-12\), the ordered pair \((0,-\frac{12}{7})\) is a solution.

If you provide the specific ordered pairs, we can check each of them one by one using the above method.