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1. Solve, using linear combination.

3x – y = 4
2x + y = 6



2. What is the y-coordinate of the solution to the system of equations?
5x - y = 25
4x + 3y = 1


3 . What is the x-coordinate of the solution to the system of equations?
x = y + 16
y + 4x = 9

4 . Graph the system of equations using technology.

What is the x-coordinate of the solution?

Round to the nearest hundredth.
-6x - 7y = 8
x + 5y = 11



Answer :

3x - y = 42x + y = 6the answer is always:y = 3x 4y = 6-2xand y = y gives:3x-4 = 6-2x, which gives:5x = 10x = 2

The x-coordinates and y-coordinates of the given simultaneous equations are; as silver below.

How to solve simultaneous equations?

1) To use linear combinations to solve the simultaneous equation;

3x – y = 4    ------(eq 1)

2x + y = 6    ---- (eq 2)

Add eq 1 to eq 2 to get;

5x = 10

divide both sides by 2 to get;

x = 2

Thus; 3(2) - y = 4

y = 6 - 4

y = 2

2) 5x - y = 25   ------(eq 1)

4x + 3y = 1   ----- (eq 2)

Make y the subject in eq 1 t get;

y = 5x - 25

Put 5x - 25 for y into the equation 2 to get;

4x + 3(5x - 25) = 1

4x + 15x = 76

19x = 76

x = 4

y = 5(4) - 25

y = -5

3) x = y + 16 - - - (eq 1)

y + 4x = 9 - - - (eq 2)

Put eq 1 in eq 2 to get;

y + 4(y + 16) = 9

y + 4y + 64 = 9

5y + 64 = 9

y = (9 - 64)/5

y = -11

Thus;

x = -11 + 16

x = 5

4) -6x - 7y = 8 - - - (eq 1)

x + 5y = 11 - - - (eq 2)

Make x the subject in eq 2 to get;

x = 11 - 5y

Put 11 - 5y for x in eq 1;

6(11-5y) -7y = 8

66 + 30y - 7y = 8

23y = -58

y = -2.5217

Thus;

x + 5(-2.5217) = 8

x = 8 + 12.608

x = 20.608

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