Question

X + y = 16 5x - 4y = 12

Answer 1

Answer:

x = 8.44, y = 7.56

Step-by-step explanation:

x + y = 16 (equation 1)

5x - 4y = 12 (equation 2)

(x + y = 16)× 5

(5x - 4y = 12) × 1

9y/9 = 68/9

y = 7.56

Substitute the value of x in equation 1

x + 7.56 = 16

x = 16 - 7.56

x = 8.44

Therefore, x = 8.44, y = 7.56

Answer 2

Answer:

x = 76 / 9 [ 8 (4 / 9) = $8.\bar{4}$ ]

y = 68 / 9 [ 7 (5 / 9) = $7.\bar{5}$ ]

__________________

Step-by-step explanation:

There are several methods that can be used to solve systems but in this situation, it is generally easier to cancel out a variable by adding the system of equations together.

This is how it's done:

x + y = 16

5x – 4y = 12

__________

4 ( x + y = 16 )

+ 5x – 4y = 12

[Multiplying the entire equation by 4 to cancel out the y because 4y – 4y = 0]

___________

4x + 4y = 64

+ 5x – 4y = 12

__________

9x = 76

÷9 ÷9

[Dividing by the coefficient of 9x in x to get x]

______

x = 76 / 9.

_______

Now that we have the x variable, you can simply substitute that quantity into x + y = 16 to solve for y.

So:

x + y = 16

[substituting the value of x into the equation]

(76 / 9) + y = 16

[Creating a common denominator that

can be canceled out]

(76 / 9) + (9y / 9) = (144 / 9)

76 + 9y = 144

[Subtracting 76 from both sides to isolate 9y]

–76 –76

__________

9y = 68

÷9 ÷9

[Dividing both sides by the coefficient of 9y in y to get y]

_________

y = 68 / 9

_________

We can also verify that these variables have the correct value because:

x + y = 16

5x – 4y = 12

→

(76 / 9) + (68 / 9) = 16

5(76 / 9) – 4(68 / 9) = 12

__________________

(76 + 68 / 9) = 16

(380 / 9) – (272 / 9) = 12

___________________

144 / 9 = 16

(380 – 272 / 9) = 12

__________________

144 / 9 × 9 = 16 × 9

108 / 9 = 12

__________________

144 = 144 ✓

108 / 9 × 9 = 12 × 9

_________________

144 = 144 ✓

108 = 108 ✓