Question

2x − 5y = 16 3x + 2y = 5 Hi! Can you please help me with this? I've tried it but I just can't seem to figure it out! If you can,please provide an explanation.Thanks,have a good day!

Answer 1

y=2 and x=3

Explanation:

2x-5y=16 equation 1

3x+2y=5 equation 2

multiplying equation 1 by 3 and equation 2 by 2 so that 6x-6x cancel each other

3(2x-5y=16) 6x-15y=48 equation 3

2(3x+2y=5) 6x+4y=10 equation 4

substracting equation 3 and equation 4

6x-15y=48

-6x-4y=-10 changing sign

-19y=38

y=-38/19

y=-2

putting the value of y in equation 1

2x-5(-2)=16

2x+10=16

2x=16-10

2x=6

x=6/2

x=3

i have checked the values these are correct

i hope this will help you :)

Answer 2

Answer: x = 3, y = -2 → (3, -2)

Explanation:

Using Elimination Method, multiply the equations by a number that allows the coefficients of either x or y to be the same number with opposite signs. Then add the two equations to solve solve for the remaining variable.

I choose to eliminate x:

2x - 5y = 16 --> 3(2x - 5y = 16) --> 6x - 5y = 48

3x + 2y = 5 --> -2(3x + 2y = 5) --> -6x - 4y = -10

-19y = 38

÷19 ÷19

y = -2

Next, substitute y = -2 into either equation to solve for x.

I choose the 1st equation:

2x - 5y = 16

2x - 5(-2) = 16

2x + 10 = 16

2x = 6

x = 3

Check your answer by inputting x = 3 and y = -2 into the other (2nd) equation:

3x + 2y = 5

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

9 + -4 = 5

5 = 5
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