Solve the system of equations 4x-2y=10 x+2y=15?

Isolate y in two equations:
4x - 2y = 10
2x - y = 5
y = 2x - 5

x + 2y = 15
y = (15 - x)/2

Value of x:
2(2x - 5) = 15 - x
4x - 10 = 15 - x
5x = 25
x = 5

Value of y—1st equation:
= 2(5) - 5
= 10 - 5
= 5

Answer: x = 5, y = 5

Proof—2nd equation:
5 + 2(5) = 15
5 + 10 = 15

The third question is easiest. x + y = 1 x - y = 1 You can answer this without doing any calculations, but I want to show you the method. Note that the coefficients of the y terms are the same except for sign: +1 and -1. That tells you that when the equations are added together, the y terms will be eliminated.    x + y = 1    x - y = 1    -----------    2x = 2 Solve for x:    2x = 2     x = 1 Now plug the x value into one of the original equations and solve for y:    x + y = 1    1 + y = 1    ∴ y = 0 ===== Do the first question the same way. ===== For the second question, rearrange the first equation so the x and y terms are on the same side of the equals side. Then solve the same way as above. ===== "Two numbers have a sum equal to 50. their difference is 16. What are the variables?" x and y such that x+y=50 and x-y=16 x=33, y=17 =====

x = y = 5

You can do this by elimination. Check out my eHow article on how to solve a system of two linear equations and two unknowns by using the elimination method:
http://www.ehow.com/how_4847235_two-unknowns-using-elimination-method.html


Add the two equations to get:
5x=25

Solve for x:
x=5

Now plug this x value into either equation and solve for y. I'll use the bottom equation, so:
5+2y=15
2y=10
y=5

So, x=5 and y=5 (answer).

Solve by using substitution.

4x - 2y = 10
x + 2y = 15

x + 2y = 15
x = (15 - 2y) ...... (1)

4x - 2y = 10

Substitute (1) for x.
4(15 - 2y) - 2y = 10
60 - 8y - 2y = 10
-10y = 10 - 60
y = -50/(-10)
y = 5

Substitute 5 for y.
x + 2y = 15
x + 2(5) = 15
x = 15 - 10
x = 5

∴ x = 5, y = 5

4X-2Y=10, X+2y=15

Solve either equation for X in terms of Y. The second is the easiest to do that.

X+2Y=15, X=-2y+15.

Substitute that solution for X in the first equation.

4 (-2Y+15) -2y = 10. -8Y + 60 -2Y = 10.

Combine the Ys. -10Y + 60 = 10. Subtract 60 from both sides.

-10Y = -50. Divide both sides by -10. Y = 5

Use Y = 5 in your second equation and solve for X.

X + 2(5) = 15, X + 10 = 15. X = 5.

easy to solve by adding the 2 equations member / member :

4x-2y + x +2y = 10+15

5x = 25

x = 5

x + 2y = 15 => 2y = 15 -x
y = 1/2 (15-x)
y = 1/2 (15-5)
y = 5

solution : x = 5, y = 5

5x = 25
x = 5

5 + 2y = 15
2y = 10
y = 5

x = 5 , y = 5

This is a very simple problem, so I'm not going to tell the answer right out

Step 1 - Add the two equations, and cancel out y. You'll get the answer for x.

Step 2 - Substitute the value of x in equation 1 - you'll get the value of y.

Here's a clue - x and y are equal.

4x - 2y = 10
x + 2y =15
-----------------
5x = 25
x = 25/5
x = 5

4x - 2y = 10
4(5) - 2y = 10
20 - 2y = 10
2y = 20 - 10
2y = 10
y = 10/2
y = 5