Question

4x - 2y = - 3
x + y = - 3
which of the following is the graph of the system of equations?
choose 1 answer

Explanation:

Step1: Rewrite equations in slope - intercept form

For the equation \(4x - 2y=-3\), solve for \(y\):
\[

$$\begin{align*} - 2y&=-4x - 3\\ y& = 2x+\frac{3}{2} \end{align*}$$

\]
The slope \(m_1 = 2\) and the \(y\) - intercept \(b_1=\frac{3}{2}\).
For the equation \(x + y=-3\), solve for \(y\):
\[y=-x - 3\]
The slope \(m_2=-1\) and the \(y\) - intercept \(b_2=-3\).

Step2: Analyze slopes and intercepts for graph

The line \(y = 2x+\frac{3}{2}\) has a positive slope of \(2\) (rises 2 units for every 1 unit run) and \(y\) - intercept above the origin (\(y=\frac{3}{2}\)). The line \(y=-x - 3\) has a negative slope of \(- 1\) (falls 1 unit for every 1 unit run) and \(y\) - intercept of \(-3\) below the origin.

Answer:

C. Option with one line having positive slope and one line having negative slope, with appropriate \(y\) - intercepts as calculated.