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Question

4x+3y=19
2x-5y=3

Show working. NOT homework!!!

Answer 1

4x+3y=19
-
(2*(2x-5y))=6
____________
3y+10y=19-6
_____________
13y=13
_____________
so, y=1.
now,
2x-5*1=3
i.e; 2x=8
or, x=4

hence, x-4;y=1.................deserve 10 pts..isn't it??

Answer 2

OK there is several method to solve this problem:

1)Linear substitution:
2) coefficient method
3) determinant method
4) matrix method

4x+3y=19
2x-5y=3

hier iets easy to use method 2)
multiply the last equation with 2 and subtract it from the first and get:
. . 4x+3y=19
- (4x-10y)=6
=========
. . . .0+13y= 13= y=1
======================
put this result in one of the equation and get:
4x+3*1=19=> 16/4=4=x
====================

Answer 3

Thanks for the question. This one is known as "a system of linear equations (with two unknowns)." Because the equations represent two lines, the "solution" is simply one of the following:

o A point: The two lines intersect; [consistent]

o Infinitely many points: The lines overlap; [dependent]

or

o Empty: The lines never touch (they are parallel) [inconsistent]

Which case do we have here? Because the lines have different slopes, we are assured that they intersect, so we have an "independent, consistent set of equations with one solution."

Let's find the point!

Eliminate one variable (I choose x) by multiplying/adding the equations:

4x+3y=19 remains unchanged ... 4x+3y=19
2x-5y=3 is multiplied by (-2) ... -4x+10y=-6

Add them together:

13y = 13
So, y = 1.

Solve for x, now, using one of the original equations:

2x - 5(1) = 3
2x = 8
x=4

Put 'em together as a coordinate pair: The solution is (4,1).

That point is where the lines intersect!

Hope this helps.

Answer 4

(1) 4x+3y=19
(2) 2x-5y=3 multiply by 2
(2a) 4x-10y=6 subtract from (1)
13y=13 divide by 13
y=1
substitute into (2)
2x-5*1=3 add 5
2x=8 divide by 2
x=4
solution is (4,1)

check
substitute into (1)
4*4+3*1=19
16+3=19

Answer 5

4x + 3y = 19.......(1)
2x - 5y = 3..........(2)

Taking equation (2)
2x - 5y = 3
--> 2x = 5y + 3...(3)

Substitute (3) into (1)

2(5y + 3) + 3y = 19
10y + 6 + 3y = 19
13y = 13
y = 1

Substitute value for y in equation (1)

4x + 3(1) = 19
4x = 16
x = 4

x = 4, y = 1

Answer 6

x=4 y=1
4x=4 times 4 =16
3y=3 times 1=3
16+3=19

Answer 7

4x+3y=19…..(1)
2x-5y=3…….(2)
multiply (2) by 2 & subtract from (1)
4x+3y-4x+10y=19-6
13y=13
y=1
put in (1)to get x

Answer 8

4x+3y=19 2x-5y=3
3y=19-4x -5y=3-2x
y=(19-4x)/3 y=(3-2x)/-5

(19-4x)/3=(3-2x)/-5
-5(19-4x)=3(3-2x)
-95+20x=9-6x
20x+6x=95+9
26x=104
x=4 y=1