Question

Solve the systme of equation
7y+10x−8=0
2y−5x−18=0
​

Answer 1

To solve the system of equations 7y + 10x - 8 = 0 and 2y - 5x - 18 = 0, first isolate y in the first equation, then substitute the value of y into the second equation and solve for x. Finally, substitute the value of x back into the first equation to solve for y.

Step-by-step explanation:

To solve the system of equations:

7y + 10x - 8 = 0

2y - 5x - 18 = 0

1. Rearrange the first equation to isolate y: 7y = -10x + 8
2. Divide both sides of the equation by 7 to solve for y: y = -10/7x + 8/7
3. Substitute this value of y into the second equation: 2(-10/7x + 8/7) - 5x - 18 = 0
4. Simplify and solve for x: -20/7x + 16/7 - 5x - 18 = 0
5. Combine like terms: -20/7x - 5x - 2 = 0
6. Combine the x terms: -35/7x = 2
7. Divide both sides by -35/7 to solve for x: x = -2 * 35/7 = -10
8. Substitute this value of x back into the first equation to solve for y: 7y + 10(-10) - 8 = 0
9. Simplify and solve for y: 7y - 100 - 8 = 0
10. Combine like terms: 7y - 108 = 0
11. Add 108 to both sides: 7y = 108
12. Divide both sides by 7 to solve for y: y = 108/7 = 15 3/7

Therefore, the solution to the system of equations is x = -10 and y = 15 3/7.

Answer 2

(2, 4)

Step-by-step explanation:

Let's solve this by elimination through addition and subtraction. Multiply the second equation by 2. The resulting system is then:

7y+10x−8=0

4y-10x - 36 = 0

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11y - 44 = 0, or 11y = 44. Solving for y, we get y = 4.

Substituting 4 for y in the 2nd equation results in:

2(4) - 5x - 18 = 0, or

-5x - 10 = 0

Then 5x = -10, or x = 2.

The solution is (2, 4)