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vladimir2022 [97]
2 years ago
10

Solve the system of linear equations by substituting. Check your solution

Mathematics
1 answer:
Ghella [55]2 years ago
8 0
QUESTION 4

The given system of linear equations are,

y = 5x - 7...(1)

and

- 3x - 2y = - 12...(2)

We put equation (1) into equation (2) to obtain,

- 3x - 2(5x - 7) = - 12

We expand to get,

- 3x - 10x + 14 = - 12

Group like terms to get,

- 3x - 10x = - 12 - 14

Simplify to get,

- 13x = - 26

Divide both sides by -13 to get,

x = 2

Put the value of x into equation (1) to get,

y = 5(2) - 7

y = 10 - 7 = 3

The solution is

x = 2 \: \: and \: \: = 3

QUESTION 5

The given system of linear equations are

-4x+y=6....(1)
and

-5x-y=21...(2)

We make y the subject in equation (1) to get,

y = 4x + 6....(3)

Put equation (3) into equation (2) to get,

- 5x - (4x + 6) = 21

We expand to get,

- 5x - 4x - 6 =21

We group like terms to get,

- 5x - 4x = 21 + 6

This implies that,

- 9x = 27

We divide both sides by -9 to get,

x = - 3

Put the value of x in to equation 3 to get,

y = 4( - 3) + 6

y = - 12 + 6 = - 6

Therefore the solution is

x = - 3 \: and \: y = - 6

QUESTION 6

The given equations are,

-7x-2y=-13...(1)

and

x-2y=-13...(2)

Make x the subject in equation (2) to get,

x = 2y - 13...(3)

Put equation (3) into equation (1) to get,
- 7(2y - 13) - 2y = - 13

We expand to get,

- 14y + 91 - 2y = - 13

We group like terms to obtain,

- 14y - 2y = - 13 - 91

.Simplify to get,

- 16y = - 104

Divide through by -16 to get,

y = \frac{13}{2}

Put the value of y into equation (3) to get,

x = 2( \frac{13}{2} ) - 13

x = 13 - 13 = 0

Therefore

x = 0 \: and \: y = \frac{13}{2}
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