Question

Solve the system using substitution.
2x - 5y = 26
X - 5y = 3

Answer 1

`\left \{ {{x=23} \atop {y=4}} \right.`

Explanation:

`\left \{ {{2x - 5y =26} \atop {x-5y=3}} \right.`

you can add 5y to both sides of the second equation:

`x = 5y + 3`

Then, substitute:

`2(5y + 3) - 5y = 26`

use the distributive property on the left side:

`10y + 6 - 5y = 26`

`5y + 6 = 26`

subtract 6 from both sides

`5y = 20`

divide both sides by 5

`y = 4`

Substitute into original equation

`x - 5y = 3 --> x - 5(4) = 3\\x - 20 = 3\\x = 23`

Answer 2

(x, y) = (23, 4)

Explanation:

2x - 5y = 26

x - 5y = 3 $\Rightarrow$ x = 3+5y

substituting the value of x ( second equation) into the first equation, we get, 2(3+5y) - 5y = 26. Simplifing, we get,

6+10y - 5y =26

5y = 20

y = 4

So, x = 3+5*4 = 3+20 = 23