ex.

5x+4y=4 and 4x+5y=31/8

I want to cancel out the y-variable so I will multiply each equation by a different number to get the same number on y. I chose to multiply the equations by 8 on one and 10 on the other to get 40y.

8 * (4x+5y=31/8) = 32x+40y=31

10 * (5x+4y=4) = 50x + 40y = 40

Then we set up a subtraction problem with the new equations we get:

50x + 40y = 40

– 32x + 40y = 31

——————————-

18x + 0y = 9

Now we have a simple equation, 18x = 9

We divide 18 by 9 (9/18 = x) and get x=1/2

Now you can plug x back into any of the two original equations to find y.

5x + 4y = 4 x=1/2

5(1/2) +4y = 4

4y = 4-(5/2)

y = 3/8

The second one is done similarly by finding a variable (x or y) to eliminate by making the number the same on both equations.

Multiply the first equation by 5 to get -35x +40y=160

Multiply the second equation by 7 to get 35x + 42y = 168

Since one of the x variables is positive and the other negative, we can add the equations together this time.

-35x +40y =160

+ 35x + 42y = 168

———————————

0x + 82y = 328

Now a simple equation of 82y = 328

Divide 82 on both sides to get y = (328/82}

so y = 4

Plug y=4 back into any of the two original equations

5x + 6y = 24 where y=4

5x + 6(4)=24

5x +24 = 24

so 5x = 0

so x = 0

If this is helpful vote for top answer!