Question

Solve this system of equations:
y = 3x
5x + 2y = 22

Answer 1

Answer:

x = 2 and y = 6.

Step by step explanation:

We can solve this system of equations by substitution or elimination method. Here's how to solve it using the substitution method:

Substitution Method:
We are given two equations:
y = 3x (Equation 1)
5x + 2y = 22 (Equation 2)

Step 1: Solve Equation 1 for y in terms of x.
y = 3x

Step 2: Substitute the value of y from Equation 1 into Equation 2.
5x + 2y = 22
5x + 2(3x) = 22

Step 3: Simplify and solve for x.
5x + 6x = 22
11x = 22
x = 2

Step 4: Substitute the value of x into Equation 1 to find y.
y = 3x
y = 3(2)
y = 6

Therefore, the solution to the system of equations is x = 2 and y = 6.

Check:
To check our solution, we substitute the values of x and y into both equations and see if they are true.

For Equation 1: y = 3x
6 = 3(2) which is true.

For Equation 2: 5x + 2y = 22
5(2) + 2(6) = 22 which is also true.

Therefore, our solution is correct.

Answer 2

3x - y = 0 ⇒ 2(3x - y = 0 ) ⇒ 6x - 2y = 0

5x + 2y = 22 ⇒ 1(5x + 2y = 22) ⇒ 5x + 2y = 22

11x = 22

x = 2

3x - y = 0 ⇒ 3(2) - y = 0 ⇒ 6 - y = 0 ⇒ 6 = y

Answer: x=2, y=6