Question

2x+3y = 17 2y + z = 1 5x +10z = 25 Find x

Answer 1

Answer:

x = 7

Step-by-step explanation:

Given the equations

2x + 3y = 17 → (1)

2y + z = 1 → (2)

5x + 10z = 25 → (3)

Rearrange (2) expressing z in terms of y

z = 1 - 2y

Substitute z = 1 - 2y into (3)

5x + 10(1 - 2y) = 25

5x + 10 - 20y = 25 ( subtract 10 from both sides )

5x - 20y = 15 → (4)

Multiply (1) by 20 and (4) by 3, then add to eliminate the y- term

40x + 60y = 340 → (5)

15x - 60y = 45 → (6)

Add (5) and (6) term by term to eliminate y, that is

55x = 385 ( divide both sides by 55 )

x = 7

Answer 2

Answer:

$x = 7$

Step-by-step explanation:

From the equation $2y + z = 1$ , we can separate $z$ so that $z = 1-2y$.

The equation $5x+10z = 25$ can then be turned into:

$5x+10(1-2y) = 25$

$5x+10-20y = 25$

$5x -20y = 15$

$x-4y = 3$ (divide by $5$ on both sides)

We can now use elimination to solve for one of the variable:

$2(x-4y) = 2\times3$ (times 2 to get $2x$ for elimination)

$2x-8y=6$

$2x+3y-(2x-8y) = 17-6$

$11y = 11$

$y = 1$

Now, we can use substitution to solve for $x$:

$2x+3y = 17$

$2x+3 = 17$

$x = 7$

Hope this helps :)