Question

2x + 3y = 45
X + Y = 10

What is the value of X of the solution for this system

Answer 1

2x+3y=45
x+y=10

Take the bottom equation and solve for y

x+y=10
Subtract x from both sides
y=-x+10

Substitute into the top equation

2x+3(-x+10)=45
2x-3x+30=45
Subtract 30 from both sides + add like terms
-x=15
Divide both sides by -1
x=-15

Answer 2

$\begin{cases}&2x + 3y = 45 ----- (1) \\&x + y = 10 ----- (2) \end{cases}$

Make x the subject for equation (2):
$\begin{cases}&2x + 3y = 45 ----- (1) \\&x = 10 - y ----- (2) \end{cases}$

Substitute equation (2) into equation (1):
$2(10-y) + 3y = 45$
$20 -2y + 3y = 45$
$20 + y = 45$
$y = 45 - 20$
$y = 25$

Subsitute y = 25 into equation (2):
$x = 10 - (25)$
$x = -15$

Answer: x = -15