Question

Solve the system of equations. y=-3x+4 -4x+y=-10​

Answer 1

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`y = - 3x + 4`

Add sides 3x

`y + 3x = 3x - 3x + 4`

`3x + y = 4`

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`1) \: 3x + y = 4`

`2) \: - 4x + y = - 10`

Multiply sides of the (( equation 2 )) by - 1

`1) \: 3x + y = 4`

`2) \: 4x - y = 10`

Add up equations

`3x + 4x + y - y = 4 + 10`

`7x = 14`

Divide sides by 7

`(7x)/(7) = (14)/(7) \\`

`x = 2`

Put the value of x in one of the (1) or (2) equations to find the value of y .

I put it in equation 1 :

`3x + y = 4`

`3(2) + y = 4`

`6 + y = 4`

`y + 6 = 4`

Subtract sides 6

`y + 6 - 6 = 4 - 6`

`y = - 2`

And we're done...

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Answer 2

Explanation:

In this particular case we have the following system of equations:

y

=

−

3

x

+

4

[

E

q

.

1

]

x

+

4

y

=

−

6

[

E

q

.

2

]

Substituting

[

E

q

.

1

]

in

[

E

q

.

2

]

:

x

+

4

(

−

3

x

+

4

)

=

−

6

Applying the distributive property on the left side:

x

−

12

x

+

16

=

−

6

Simplifying

:

−

11

x

=

−

22

Solving for

y

:

x

=

−

22

−

11

=

2

Substituting

x

=

2

in

[

E

q

.

1

]

:

y

=

−

3

(

2

)

+

4

=

−

2

Therefore

, the solutions are

x

=

2

and

y

=

−

2