Test: Substitution Method - Year 10 MCQ

0.2x + 0.3y = 1.2
2x+3y=12   …..(1)
0.1x – 0.1y = 0.1​x-y=1  ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3

3x-y+9=0 …(1)
3x+4y-6=0  …(2)​
From 1
3x=y-9
Substituting in 2
y-9+4y-6=0
5y-15=0
y=3
x=-2

2x-y+6=0
y=2x+6   ….(1)
4x+5y-16=0​
Substituting the values
4x+5(2x+6)-16=0
14x+14=0
x=-1
y=4

Alright, we have a system of two linear equations with two variables, p and q. Let's write them down:

1) 2p + 3q = 9
2) p - q = 2

Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.

First, we'll solve the second equation for one of the variables. Let's solve for p:

p = q + 2

Now, we'll substitute this expression for p into the first equation:

2(q + 2) + 3q = 9

Distribute the 2:

2q + 4 + 3q = 9

Combine like terms:

5q + 4 = 9

Now, solve for q:

5q = 9 - 4
5q = 5
q = 1

Now that we have the value for q, we can plug it back into the expression for p:

p = q + 2
p = 1 + 2
p = 3
 

2x-5y+4=0…(I)

2x+y-8=0…(II)

From the equation II we get,

y=-2x+8

Substituting this value of y in equation II we get,

2x-5(-2x+8)+4=0

⇒12x -36=0

⇒x=3

Substituting this value of x in equation II we get,

y=2

Hence the solution is (3, 2).

Solution:

- Let's assume the smaller number is x.
- According to the given condition, the larger number is twice the smaller number, so it can be expressed as 2x.
- The sum of the two numbers is 45, so we can write the equation as: x + 2x = 45
- Combining like terms, we get 3x = 45
- Dividing both sides by 3, we find x = 15

Therefore, the smaller number is 15. So, the correct answer is C: 15.

 The correct answer is a.

x-2y = 6 

2x+y = 17​

2x - 4y = 12

2x + y  = 17

 -5y   =   -5

 y  =  1

x-2(1) = 6

x= 8

When we are given only one equation and two variables we assume values for one variable and find the values for the other variable.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.