5x+6y=2 6x+2y=18 Solve by elimination

5x + 6y = 2 \\

6x + 2y = 18 \\

[SOLUTION]

x = \frac{55}{28}, \quad y = -\frac{16}{28}

[STEP-BY-STEP]

1. Multiply the first equation by 2:

2(5x + 6y) = 2(2)

10x + 12y = 4 \quad \text{(Equation 3)}

2. Multiply the second equation by 6:

6(6x + 2y) = 6(18)

36x + 12y = 108 \quad \text{(Equation 4)}

3. Subtract Equation 3 from Equation 4:

(36x + 12y) - (10x + 12y) = 108 - 4

26x = 104

4. Solve for \( x \):

x = \frac{104}{26}

x = \frac{52}{13}

x=4

5. Substitute \( x = 4 \) back into the original first equation:

5\times4+6y=2

20+6y=2

6. Solve for \( y \):

6y=2-20

6y=-18

y=-3

7. Answer:

x=4,y=-3