How do you solve the system of equations -8x - 2y = - 1 and 3x - 12y = 4?

2 Answers

x=10/51 & y=-29/102

Explanation:

Given system of linear equations:

-8x-2y=-1

or 8x+2y=1\ ...... .......(1)

3x-12y=4\ ...... .......(2)

Multiplying (1) by 6 & adding to (2) as follows

3x-12y+6(8x+2y)=4+6\times 1

51x=10

x=10/51

setting x=10/51 in (1) we get

y=\frac{1-8x}{2}=\frac{1-8\times 10/51}{2}=-29/102

hence, the solution is x=10/51 & y=-29/102

Jul 7, 2018

x=10/51

y=-29/102

Explanation:

color(blue)("Equation A: ") -8x-2y=-1

color(green)("Equation B: ") 3x-12y=4

Multiply color(blue)("Equation A") by 6, then use elimination to first eliminate y from each equation.

color(blue)("Equation A: ") 6*(-8x-2y) = 6*(-1)

color(blue)("Equation A: ") -48x-12y=-6

color(green)("Equation B: ") 3x-12y=4

Subtract color(green)("Equation B") from color(blue)("Equation A"):

-51x = -10

x = 10/51

Substitute this x value into one of the original equations to find y:

-8(10/51) - 2y =-1

-2y = -1 + 80/51

y = 1/2 - 40/51

y = frac{51-80}{102}

y = -29/102