Solve the linear systems:

1)
\[
0.5x + 4y = 16
\]
\[
y = -16
\]

2)
\[
3x + 6y = 15
\]
\[
-2x + 3y = -3
\]

3)
\[
7y = -14x + 42
\]
\[
7y = 14x + 14
\]

1.5x+4y=16 5x+4(-16)=16 5x-64=16 5x=80 x=16
2.3x+6y=15 -2x+3y=-3
Multiply the 2nd equation by 2
3x+6y=15 -4x+6y=-6 7x=9 x=9/7
3x+6y=15 3(9/7)+6y=15 27/7+6y=15 6y=78/7 y=78/42 or 39/21 or 13/7
3.7y = -14x + 42 7y = 14 x + 14
-14x+42=14x+14 -28x=-28 x=1

Answered by deathstrike001 | 2024-06-10

1 ) { 5 x + 4 y = 16 y = − 16 ​ { 5 x + 4 ∗ ( − 16 ) = 16 y = − 16 ​ { 5 x − 64 = 16 y = − 16 ​
{ 5 x = 16 + 64 y = − 16 ​ { 5 x = 80/ : 5 y = − 16 ​ { 5 x = 16 + 64 y = − 16 ​ { x = 16 y = − 16 ​
2 ) { 3 x + 6 y = 15 − 2 x + 3 y = − 3 ​ { 3 x = 15 − 6 y / : 3 − 2 x + 3 y = − 3 ​ { x = 5 − 2 y − 2 ∗ ( 5 − 2 y ) + 3 y = − 3 ​ { x = 5 − 2 y − 10 + 4 y + 3 y = − 3 ​
{ x = 5 − 2 y 7 y = − 3 + 10 ​ { x = 5 − 2 y 7 y = 7 / : 7 ​ { x = 5 − 2 ∗ 1 y = 1 ​ { x = 3 y = 1 ​
3 ) { 7 y = − 14 x + 42 7 y = 14 x + 14/ : 7 ​ { 7 ∗ ( 2 x + 2 ) = − 14 x + 42 y = 2 x + 2 ​ { 14 x + 14 = − 14 x + 42 y = 2 x + 2 ​ { 14 x + 14 x = 42 − 14 y = 2 x + 2 ​
{ 28 x = 28 / : 28 y = 2 x + 2 ​ { x = 1 y = 2 ∗ 1 + 2 ​ { x = 1 y = 4 ​

Answered by Lilith | 2024-06-10

The solutions to the systems of equations are:

(160, -16)
(3, 1)
(1, 4).

;

Answered by deathstrike001 | 2024-10-11