Solve the systems of equations 1) { <mtable columnalign="left left" rowspacing=".2em" c

Layla Velazquez

Layla Velazquez

Answered question

2022-06-15

Solve the systems of equations
1) { 4 x 3 y = 1 3 x + 4 y = 6
2) { 3 x 2 y = 1 x + 2 y = 3
3) { 3 x + 6 y = 6 2 x + 4 y = 4
4) { 3 x + 6 y = 3 5 x 10 y = 5

Answer & Explanation

Dustin Durham

Dustin Durham

Beginner2022-06-16Added 31 answers

1) { 4 x 3 y = 1 3 x + 4 y = 6

Multiply by 3 and 4 in the first equation and second equation respectively and then add obtained equations to obtain the value of y.
3 × ( 4 x 3 y ) = 3 × ( 1 )
12 x 9 y = 3
and
4 × ( 3 x + 4 y ) = 4 × 6
12 x + 16 y = 24

Now,
( 12 x 9 y ) + ( 12 x + 16 y ) = 3 + 24
12 x 9 y 12 x + 16 y = 21
7 y = 21
y = 3

Substitute the value y in the equation 4 x 3 y = 1 to obtain the value of x.
Now,
4 x 3 × 3 = 1
4 x 9 = 1
4 x = 1 + 9
4 x = 8
x = 2

Hence, the solution is ( 2 , 3 ) .

2) { 3 x 2 y = 1 x + 2 y = 3

Add both equations to obtain the value of x.
3 x 2 y + ( x + 2 y ) = 1 + 3
3 x 2 y x + 2 y = 2
2 x = 2
x = 1

Substitute the value of x in the second equation 1 + 2 y = 3
y = 2

Thus, the solution is ( 1 , 2 )

3) { 3 x + 6 y = 6 2 x + 4 y = 4

Now, 3 2 = 6 4 6 4
Thus, there is no solution for this system.
juanberrio8a

juanberrio8a

Beginner2022-06-17Added 7 answers

4) Given: { 3 x + 6 y = 3 5 x 10 y = 5
3 5 = 6 10 = 3 5
Thus, we get infinitely solution.

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