Solve this system algebraically. 7x - 2y = 4; 5y + 3x = 10

Solution:

Given,

7x - 2y = 4 --- (1)

5y + 3x = 10 --- (2)

Consider equation (2),

Subtract 3x from both sides giving:

5y = 10 - 3x

Divide both sides by 5

y = 10/5 - 3x/5 --- (3)

Substitute (3) in (1)

7x - 2(10/5 - 3x/5) = 4

7x - 4 + 6/5x = 4

41/5x - 4 = 4

41/5x = 8

x = 40/41

Substitute x = 40/41 in (2)

5y + 3(40/41)= 10

5y +120/41 = 10

5y = 10 - 120/41

y = 58/41

Therefore,

x = 40/41

y = 58/41

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Solve this system algebraically. 7x - 2y = 4; 5y + 3x = 10

Summary:

Solving this 7x - 2y = 4; 5y + 3x = 10 algebraically, we get x = 40/41 and y = 58/41.