Question

Please solve this system of equations.
5x-2y=9
12x-8y=4

Answer 1

(4,11/2)

Explanation:

5x-2y=9

12x-8y=4

A quick look will tell us that neither the x- nor the y- coefficient is the same in both equations, so combining the two by addition or subtraction. We can see that 2 is a multiple of 8, since 2 x 4 = 8. We should multiply the first equation by 4.

4(5x-2y=9)

Now we need to decide if we should add or subtract the equations.

20x-8y=36

12x-8y=4

Since we need to have a -8 and a +8 to eliminate the variables, we should subtract them. Change all the signs of the second equation and combine.

20x-8y=36

-12x-8y=4

----------------

8x=32

Divide both sides by 8 to get the x-value:

`(8x)/(8) = (32)/(8)`

x=4

Now that we have our x-value, we need to plug in the y-value.

5x-2y=9

5(4)-2y=9

20-2y=9

-2y=-11

y=11/2

So our solution is (4,11/2)

Let's check our work.

5x-2y=9

5(4)-2(11/2)=9

20-22/2=9

20-11=9

9=9

12x-8y=4

12(4)-8(11/2)=4

48-88/2=4

48-44=4

4=4

Our solution is correct.

Answer 2

x=4,y=11/2

Explanation:

5x−2y=9

12x−8y=4

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

5x−2y=9,12x−8y=4

To make 5x and 12x equal, multiply all terms on each side of the first equation by 12 and all terms on each side of the second by 5.

12×5x+12(−2)y=12×9,5×12x+5(−8)y=5×4

Simplify.

60x−24y=108,60x−40y=20

Subtract 60x−40y=20 from 60x−24y=108 by subtracting like terms on each side of the equal sign.

60x−60x−24y+40y=108−20

Add 60x to −60x. Terms 60x and −60x cancel out, leaving an equation with only one variable that can be solved.

−24y+40y=108−20

Add −24y to 40y.

16y=108−20

Add 108 to −20.

16y=88

Divide both sides by 16.

y=11/2

Substitute 11/2 for y in 12x−8y=4. Because the resulting equation contains only one variable, you can solve for x directly.

12x−8x11/2=4

Multiply −8 times 11/2.

12x−44=4

Add 44 to both sides of the equation.

12x=48

Divide both sides by 12.

x=4

The system is now solved.

x=4,y=11/2