Question

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Answer 1

The correct location of the system of equations are;

Single solution;

y = 11 - 2•x

4•x - y = 7

x + y = 15

2•x - y = 15

No solution;

2•x + y = 7

-4•x = 2•y + 14

x = 12 - 3•y

3•x + 9•y = 24

Infinite solution;

2•x + y = 7

-6•x = 3•y - 21

What are the types of solutions to linear system of equations?

The possible system of equations and their solution are presented as follows;

System of equations

• y = 11 - 2•x
• 4•x - y = 7

Solution;

4•x - y = 7

Therefore;

11 - 2•x = 4•x - 7

6•x = 18

x = 3; Single solution;

System of equations

• 2•x + y = 7
• -4•x = 2•y + 14

Solution;

2•x + y = 7 gives;

y = 7 -2•x

-4•x = 2•y + 14 gives;

y = -2•x - 7

7 -2•x = -2•x - 7

0 = 14, no solution

System of equations

• x = 12 - 3•y
• 3•x + 9•y = 24

Solution;

x = 12 - 3•y gives;

3•x + 9•y = 24 gives;

x = (24 - 9•y) ÷ 3 = 8 - 3•y

Which gives;

12 - 3•y = 8 - 3•y

• 12 = 8 no solution

System of equations

• 2•x + y = 7
• -6•x = 3•y - 21

Solution;

2•x + y = 7 gives;

y = 7 - 2•x

-6•x = 3•y - 21 gives;

3•y = 21 - 6•x

y = 7 - 2•x

7 - 2•x = 7 - 2•x Infinitely many solutions

System of equations

• x + y = 15
• 2•x - y = 15

Solution;

x + y = 15 gives;

y = 15 - x

2•x - y = 15 gives;

y = 2•x - 15

Which gives;

15 - x = 2•x - 15

3•x = 15 + 15 = 30

x = 30 ÷ 3 = 10 Single solution

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