# How do solve an elimination problem using both 3x+2y=31 and 2x-y=2

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

I suggest you to eliminate variable y, hence you need to multiply by 2 the equation `2x - y = 2`  such that:

`2*(2x-y) = 4 =gt 4x - 2y = 4`

You need to add this equation to the first equation `3x + 2y = 31 ` such that:

`4x - 2y + 3x + 2y = 4 + 31`

Reducing like terms yields:

`7x = 35 =gt x = 5`

You need to substitute 5 for x in any of two equations to find y such that:

`2*5 - y = 2 =gt -y = 2 - 10 =gt -y = -8 =gt y = 8`

Hence, evaluating the solution to simultaneous equations using elimination of variable yields x = 5, y = 8.

etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Multiply the second equation by 2.

3x + 2y = 31

4x - 2y  =   4

7x = 35

divide by seven

x = 5

substitude x = 5 in the first equation.

3*5 + 2y = 31

subtract 15 from both sides

2y = 31 - 15 = 16

divide by 2

y = 8

substitute x = 5 and y = 8 in the second equation of check the results.

2*5 - 8 = 2 or 10-8 = 2

So the solution is x = 5 and y = 8