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Solve this system of linear equations:

[tex]\[ 4x - 2y = 8 \][/tex]
[tex]\[ y = \frac{3}{2}x - 2 \][/tex]

1. Plot the [tex]\( x \)[/tex]-intercept of the first equation.
2. Plot the [tex]\( y \)[/tex]-intercept of the first equation.
3. Plot the [tex]\( y \)[/tex]-intercept of the second equation.

The correct points are shown:

[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -4 \\
2 & 0 \\
\hline
\end{array}
\][/tex]



Answer :

GinnyAnswer
To solve the given system of linear equations and find the intercepts step-by-step, we need to determine the x-intercept and y-intercept for the equations [tex]\(4x - 2y = 8\)[/tex] and [tex]\( y = \frac{3}{2}x - 2\)[/tex].

### Step 1: Plot the [tex]\(x\)[/tex]-intercept of the first equation.

For the x-intercept, set [tex]\(y = 0\)[/tex] in the first equation:
[tex]\[ 4x - 2(0) = 8 \][/tex]
[tex]\[ 4x = 8 \][/tex]
[tex]\[ x = 2 \][/tex]

So, the x-intercept of the first equation is [tex]\((2, 0)\)[/tex].

### Step 2: Plot the [tex]\(y\)[/tex]-intercept of the first equation.

For the y-intercept, set [tex]\(x = 0\)[/tex] in the first equation:
[tex]\[ 4(0) - 2y = 8 \][/tex]
[tex]\[ -2y = 8 \][/tex]
[tex]\[ y = -4 \][/tex]

So, the y-intercept of the first equation is [tex]\((0, -4)\)[/tex].

### Step 3: Plot the [tex]\(y\)[/tex]-intercept of the second equation.

For the y-intercept, set [tex]\(x = 0\)[/tex] in the second equation:
[tex]\[ y = \frac{3}{2}(0) - 2 \][/tex]
[tex]\[ y = -2 \][/tex]

So, the y-intercept of the second equation is [tex]\((0, -2)\)[/tex].

### Summary of the Intercepts

Based on the steps above, the correct intercept points are:

1. [tex]\(x\)[/tex]-intercept of the first equation: [tex]\((2, 0)\)[/tex]
2. [tex]\(y\)[/tex]-intercept of the first equation: [tex]\((0, -4)\)[/tex]
3. [tex]\(y\)[/tex]-intercept of the second equation: [tex]\((0, -2)\)[/tex]

Thus, the points are:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -4 \\ 2 & 0 \\ 0 & -2 \\ \hline \end{array} \][/tex]

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