Question

Solve the following system of equations for and for y: System of Equations: Value of Value of y y=93 y = 31-3 Solve the following system of equations for a and for b: Value of a value of b System of Equations: 9 30 8 + 4 28 Plot the following system of equations on the following graph. System of Equations: P-6-20 p=2+ Note: Use the orange line (square symbols) to plot the first equation, and use the blue line (circle symbols) to plot the second equation. The values of and that solve these two equations simultaneously can be seen on the graph as Grade Now Continue without saving

Answer 1

Answer

The system of equations are as follows;

y = 9 + 3z......(1)

y = 51 - 3z.....(2)

Subtracting equation(2) from equation(1), we get,

y - y = (9 + 3z) - (51 - 3z)

Or, 0 = 9 + 3z - 51 + 3z

Or, 0 = 6z - 42

Or, 6z - 42 = 0

Or, 6z = 42

Or, z = 7

Now, putting the value of 'z' in equation(1), we get,

y = 9 + 3 * 7

Or, y = 9 + 21

Or, y = 30

So, Value of z = 7 ; Value of y = 30

System of Equations	Value of z	Value of y
y = 9 + 3z y = 51 - 3z	7	30

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The system of equations are as follows;

9a + 3b = 30.......(1)

8a + 4b = 28.......(2)

Multiplying equation(1) by the co-efficient of 'a' of equation(2), i.e. '8', we get,

(9a + 3b = 30) * 8

Or, 72a + 24b = 240.....(1')

Multiplying equation(2) by the co-efficient of 'a' of equation(1), i.e. '9', we get,

72a + 36b = 252.......(2')

Now, subtracting equation(2') from equation(1'), we get,

(72a + 24b) - (72a + 36b) = 240 - 252

Or, 72a + 24b - 72a - 36b = -12

Or, 24b - 36b = -12

Or, -12b = -12

Or, b = -12 / - 12

Or, b = 1

Now, putting the value of 'b' in equation(1), we get,

9a + 3 * 1 = 30

Or, 9a + 3 = 30

Or, 9a = 30 - 3

Or, 9a = 27

Or, a = 27 / 9

Or, a = 3

So, Value of a = 3 ; Value of b = 1

System of Equations	Value of a	Value of b
9a + 3b = 30 8a + 4b = 28	3	1

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The system of equations are as follows;

p = 6 - 2q......(1)

p = 2 + q.....(2)

Now, let us build two tables for above two equations;

Table-1 for equation, p = 6 - 2q

q	p
0	6
1	4
2	2
3	0

Table-2 for equation,.p = 2 + q

q	p
0	2
1	3
2	4
3	5
4	6
5	7
6	8
7	9
8	10
11	13
12	14

Based on the above tables, we get the following graph;

12 678 9 10

The values of p and q that solve these two equations simultaneously can be seen on the graph as p=3.3(approx), q = 1.3(approx.).

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