Question

The solution set of the following equations 2x-y=8 , 3x+2y=5 is ..............
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Answer 1

Answer is ( 3, -2 ) solution to the given set of equations

Step by step

We can use elimination method for this set of standard equations

2x-y=8 EQ.1
3x+2y=5 EQ.2

We can multiple each term in EQ.1 by 2 to eliminate y

2(2x - y = 8)
4x -2y = 16

we can add the equations and eliminate y

4x -2y = 16 EQ.1
3x+2y=5 EQ.2
——————
7x = 21

Divide both sides by 7 to solve x

7/7x = 21/7

x = 3

Now substitute value of x = 3 into EQ.2

3x+2y=5 EQ.2
3(3) + 2y = 5
9 + 2y = 5
Subtract 9 from both sides to isolate y
9-9+ 2y = 5 -9
Simplify
2y = -4
Divide both sides by 2 to solve y

2/2y = -4/2

y= -2

Your solution set is ( 3, -2 )

Check your work, sub x and y values into EQ.2

3x+2y=5 EQ.2

3(3) + 2(-2) = 5
9 - 4 = 5
5 = 5

This equals so your solution is correct!

Answer 2

x = 3,

y = -2

Explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2