How do you solve 2x+3y=10 5x-2y=8?

Question

Solve using systems of equations using elimination.

Answer 1

4x + 6y = 20
15x - 6y = 24-----ADD
19x = 44
x = 44/19

88/19 + 3y = 10
3y = 190/19 - 88/19
3y = 102/19
y = 34/19

x = 44/19 , y = 34/19

Answer 2

You can add equations vertically if you notice that the x in the top and the -x in the bottom would cancel to help you solve for y. x + 3y = -7 -x + 2y = -8 would be x - x + 3y + 2y = -7 -8 5y = -15 y = -5, then plug in for y in either equation to find x x + 3*-5 = -7 x -15 = -7 x = 8 If need be, you can multiply one equation through by 2 or some other number to make the coefficients of x or y equal so you can add them together to eliminate one variable. 4x - y = -5 -2x + 3y = 10, multiply this one by 2, OR the top one by 3, then add them together. 4x - y = -5 -4x + 6y = 20 4x - 4x - y + 6y = -5 + 20 5y = 15 y = 3 4x - 3 = -5 4x = -2 x = -1/2 Try to do the rest on your own using these 2 as a model.

Answer 3

OK - two equations, two unknowns

2x + 3y =10
5x - 2y =8 ; let multiply the top by 2 and the bottom by 3

4x + 6y = 20
15x -6y = 24; add the two equations

19x = 44
x = 44/19 or 2 6/19

Now substitute: 2(44/19) + 3y = 10
88/19 + 3y = 10
3 y = 102/19
y = 34/19 or 1 15/19

Let's check to make sure

5(44/19) - 2(34/19) = 8??
220/19 - 68/19 = 8??
152/19 = 8 ??
8 = 8 YES!!!

Hope this helps.

Answer 4

Okay so you have two equations.

2x+3y=10
5x-2y=8

You want to eliminate one term so that when you add the two equations there is just one variable.

Well in this equation I think it'd be wise to get rid of the y's because in one equation, there are positive y's and one in equation there are negative y's.

multiply the first equation by 2 and the second by 3.
[2x+3y=10] *2
[5x-2y=8]*3

You get:
4x+6y=20
15x-6y=24

Add these straight down.

19x+0y= 44
19x=44
x= 44/19

Now plug in this x in one of your equations to find y.

Let's just plug it into the first equation:
2x+3y=10
2(44/19)+3y=10
multiply
88/19 +3y = 10
get 3y by itself on one side by subtracting 88/19 on both sides
3y=10 - 88/19
rewrite 10 as a fraction over 19
3y= 190/10 - 88/19
3y= 102/19
multiply both sides by 1/3
y= (102/19 )(1/3)
y= 102/ (19*3)
y= 102/ 57
This reduces to y= 34/19

so your answer is (44/19 , 34/19)

Answer 5

solve the first equation for either x or y

2x + 3y = 10
2x = 10 - 3y
x = (10 - 3y)/2

then put in what you just got for x into the second equation

5x - 2y = 8
5((10 - 3y)/2) - 2y = 8
solve for y
5(10/2 - 3y/2) - 2y = 8
5(10/2) - 5(3y/2) -2y = 8
5(5) - (15y/2) -2y = 8
25 - 7.5y - 2y = 8
-7.5y - 2y = 8 - 25
-9.5y = -17
y= -17/-9.5

now that you know y...put it into the first equation to find a number value for x

2x + 3y = 10
2x + 3(-17/-9.5) = 10
2x = 10 - 3(-17/-9.5)
2x = 10 - 5.37
2x = 4.63
x= 4.63/2
x = 2.315

thats your x value


hope that helped!

Answer 6

2x+3y=10
5x-2y=8
Mult. Eq.1 by 2, Eq.2 by 3
4x+6y=20
15x-6y=24
--------------- Add
19x=44
x=44/19

Using 2x+3y=10,
2(44/19)+3y=10
88/19+3y= 190/19
3y=190/19-88/19
3y=102/19
y=102/19(3)
y=102/57

Verify: Using 2x+3y=10,
2(44/19)+3(102/57)=10
88/19+306/57=10
264/57+306/57=10
570/57=10
10=10

Answer 7

2x+3y = 10 -----------(1)

5x - 2y=8 -------------(2)

multiply (1) with 5 and (2) with 2

10x +15y = 50 -------(3)

10x - 4y = 16 ---------(4)

subtract(4) from (5)

19y = 34

y = 34/19

substitute y value in (1)

2x + 3(34/19) = 10

38x + 102 = 190

38x = 88

x = 88/38 = 44/19

x= 44/19 and y = 34/19

Answer 8

2x+3y=10 [*2]
5x-2y=8 [*3]
-----------------------------------
4x+6y=20
15x-6y=24
-------------------
19x=44 add
-------------------
x=44/19


2x+3y=10. substitute the value of x in this eqn:
2*44/19+3y=10
88/19+3y=10
3y=10-88/19
3y=(190-88)/19
3y=102/19
y=102/ 57
[simplify for a fraction least value]

Answer 9

2.5(2x+3y=10)
5x-2y=8

5x+7.5y=25
5x-2y=8

(5-5)x+[7.5-(-2)]y=(25-8)
9.5y=17
y=(17/9.5)=34r19

5x-2y=8
5x=8+2(34r19)
x=[8+2(34r19)]/5
=[152r19+68r19]/5
=[(152+68)r19]/5
=(220r19)/5
=44r19

therefore:
y=34r19
x=44r19

to check:
2x+3y=10
2(44r19)+3(34r19)=10
88r19+102r19=10
(88+102)r19=10
190r19=10
10=10

Answer 10

x = 5
y = 3/10 or 3.5

x=5/8 0r 1.6
y= -4

just divide.