Answered

IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.

Find two pairs of coordinates for each equation by making a T-chart. Use the coordinates to graph the lines and find the solution.

[tex]\[
\begin{array}{l}
y = 3x - 15 \\
x + y = 13
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step.

### Step 1: Create T-charts for both equations

#### Equation 1: [tex]\( y = 3x - 15 \)[/tex]

To create a T-chart, we substitute different values of [tex]\( x \)[/tex] and compute the corresponding values of [tex]\( y \)[/tex]:

| [tex]\( x \)[/tex] | [tex]\( y = 3x - 15 \)[/tex] | [tex]\( (x, y) \)[/tex] |
|--------|-------------------|------------|
| 0 | [tex]\( 3(0) - 15 = -15 \)[/tex] | (0, -15) |
| 1 | [tex]\( 3(1) - 15 = -12 \)[/tex] | (1, -12) |
| 2 | [tex]\( 3(2) - 15 = -9 \)[/tex] | (2, -9) |
| 3 | [tex]\( 3(3) - 15 = -6 \)[/tex] | (3, -6) |
| 4 | [tex]\( 3(4) - 15 = -3 \)[/tex] | (4, -3) |

We have the points: [tex]\((0, -15)\)[/tex], [tex]\((1, -12)\)[/tex], [tex]\((2, -9)\)[/tex], [tex]\((3, -6)\)[/tex], [tex]\((4, -3)\)[/tex].

#### Equation 2: [tex]\( x + y = 13 \)[/tex]

Similarly, substituting different values of [tex]\( x \)[/tex] and computing [tex]\( y \)[/tex]:

| [tex]\( x \)[/tex] | [tex]\( y = 13 - x \)[/tex] | [tex]\( (x, y) \)[/tex] |
|--------|-------------------|------------|
| 0 | [tex]\( 13 - 0 = 13 \)[/tex] | (0, 13) |
| 1 | [tex]\( 13 - 1 = 12 \)[/tex] | (1, 12) |
| 2 | [tex]\( 13 - 2 = 11 \)[/tex] | (2, 11) |
| 3 | [tex]\( 13 - 3 = 10 \)[/tex] | (3, 10) |
| 4 | [tex]\( 13 - 4 = 9 \)[/tex] | (4, 9) |

We have the points: [tex]\((0, 13)\)[/tex], [tex]\((1, 12)\)[/tex], [tex]\((2, 11)\)[/tex], [tex]\((3, 10)\)[/tex], [tex]\((4, 9)\)[/tex].

### Step 2: Graph the points and find the intersection

Plotting these points on a graph, we can draw the lines for the equations:

- For [tex]\( y = 3x - 15 \)[/tex], draw a line passing through the points [tex]\((0, -15)\)[/tex], [tex]\((1, -12)\)[/tex], [tex]\((2, -9)\)[/tex], [tex]\((3, -6)\)[/tex], [tex]\((4, -3)\)[/tex].
- For [tex]\( x + y = 13 \)[/tex], draw a line passing through the points [tex]\((0, 13)\)[/tex], [tex]\((1, 12)\)[/tex], [tex]\((2, 11)\)[/tex], [tex]\((3, 10)\)[/tex], [tex]\((4, 9)\)[/tex].

### Step 3: Find the solution at the intersection

The solution to the system of equations is where these two lines intersect. By examining our coordinates and graph, we find that the intersection of the two lines occurs at the point [tex]\((7, 6)\)[/tex].

### Summary
- T-chart for [tex]\( y = 3x - 15\)[/tex]: [tex]\((0, -15)\)[/tex], [tex]\((1, -12)\)[/tex], [tex]\((2, -9)\)[/tex], [tex]\((3, -6)\)[/tex], [tex]\((4, -3)\)[/tex].
- T-chart for [tex]\( x + y = 13\)[/tex]: [tex]\((0, 13)\)[/tex], [tex]\((1, 12)\)[/tex], [tex]\((2, 11)\)[/tex], [tex]\((3, 10)\)[/tex], [tex]\((4, 9)\)[/tex].
- The intersection point (solution) is [tex]\((7, 6)\)[/tex].

Thus, the solution to the system of equations is [tex]\((7, 6)\)[/tex].
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.