Question

Writing a System of Equations from Tables

A 2 column table with 5 rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 6, negative 4.5, negative 3, negative 1.5. A 2 column table with 5 rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 6.1, 2.1, negative 1.9, negative 5.9.

Complete the statements about the system of linear equations represented by the tables.

The equation representing the left table is

.

The equation representing the right table is

.

The solution to the system of equations is

.

Answer 1

Explanation:

`\\\begin{array}cx&y&\Delta y&x&y&\Delta y\\---&---&---&---&---&---\\0&-6&-1.5&0&6.1&-4\\1&-4.5&-1.5&1&6.1&-4\\2&-3&-1.5&2&-1.9&-4\\3&1.5&-1.5&3&-5.9&-4\\---&---&---&---&---&---\\\end {array}\\\\Tables\ representent\ lines\\\\First\ line: \ passing\ through\ (0,-6)\ and\ (2,-3)\:\\\\y+6=\frac{3} {2} (x-0) \ or\ y=\frac{3} {2} x-6\\\\\\Second \ line: \ passing\ through\ (0,6.1)\ and\ (1,2.1\:\\\\y-6.1=-4(x-0) \ or\ y=-4x+6.1\\\\Solution\ of\ the\ system\\\\`

`\Bigg\{\begin{array}{ccc}y&=&(3)/(2)x-6 \\y&=&-4x+6.1\\\end {array} \right.\\\\\\\Bigg\{\begin{array}{ccc}y&=&-4x+6.1\\(3)/(2)x-6&=&-4x+6.1 \\\end {array} \right.\\\\\\\Bigg\{\begin{array}{ccc}x&=&2.2\\y&=&-2.7 \\\end {array} \right.\\\\`

Answer 2

The equation representing the left table is ✔ y = 1.5x – 6 The equation representing the right table is ✔ y = –4x + 6.1 The solution to the system of equations is ✔ (2.2, –2.7)