Answer:
The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.
Step-by-step explanation:
<em>1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.</em>
<em>Solve these linear equations simultaneously</em>
<em>Step 1 : Find y in terms of x from any one equation</em>
6x - 5y = 8
y = <u>8 - 6x</u>
-5
<em>Step 2 : Substitute y in terms of x from step 1 in the second equation.</em>
16x - 6y = 22
16x - 6 (<u>8 - 6x)</u> = 22
-5
80x - 48 + 36x = 22 x -5
94x = 43
x = 0.457
<em>This statement is incorrect as it does have a solution.</em>
<em>2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.</em>
<em>Solve these linear equations simultaneously</em>
<em>Step 1 : Find y in terms of x from any one equation</em>
7x + 2y = 6
y = <u>6 - 7x</u>
2
<em>Step 2 : Substitute y in terms of x from step 1 in the second equation.</em>
14x + 4y = 16
14x + 4(<u>6 - 7x)</u> = 16
2
14x + 12 - 14x = 16
0 ≠ 4
<em>This statement is not true as there are no solutions.</em>
<em>3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.</em>
<em>Solve these linear equations simultaneously</em>
<em>Step 1 : Find x in terms of y from any one equation</em>
8x - 3y = 10
x = <u>10 + 3y</u>
8
<em>Step 2 : Substitute x in terms of y from step 1 in the second equation.</em>
16x - 6y = 22
16(<u>10 + 3y)</u> - 6y = 22
8
20 + 6y - 6y = 2
0 ≠ -18
<em>This statement is true because there are no solutions</em>
<em>4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.</em>
<em>Solve these linear equations simultaneously</em>
<em>Step 1 : Find x in terms of y from any one equation</em>
9x + 6y = 14
x = <u>14 - 6y</u>
9
<em>Step 2 : Substitute x in terms of y from step 1 in the second equation.</em>
18x + 12y = 26
18 (<u>14 - 6y)</u> + 12y = 26
9
8 - 12y + 12y = 26
0 ≠ 18
<em>This statement is incorrect because there are no solutions. It does not have infinite number of solutions.</em>
<em>!!</em>
