Question

Solve the simultaneous equations
below using elimination.
2y + x = 7
y + x = 5

Answer 1

The solution is x = 3 and y = 2, which can be verified by substituting back into the original equations.

Step-by-step explanation:

Given the equations:

1. 2y + x = 7
2. y + x = 5

We aim to eliminate one variable to solve for the other. We can subtract the second equation from the first to eliminate the x variable.

Step 1: Subtract equation (2) from equation (1)

• (2y + x) - (y + x) = 7 - 5
• 2y - y = 2
• y = 2

Step 2: Substitute the value of y into one of the original equations to solve for x.

• Substituting into equation (2):
• y + x = 5
• 2 + x = 5
• x = 5 - 2
• x = 3

So the solution to the simultaneous equations is x = 3 and y = 2.

Check the Solution:

Insert x and y into both original equations to check.

• For equation (1): 2(2) + 3 = 7 ✔
• For equation (2): 2 + 3 = 5 ✔

Both check out, so the solution is indeed correct.

Answer 2

y = 2; x = 3

Step-by-step explanation:

We can start by multiplying the first equation by -1.

This will allow us to eliminate the xs when we add the two equations since -x + x = 0:

-(2y + x = 7)

-2y - x = -7

Solving for y:

Now, we can solve for y by adding -2y - x = -7 and y + x = 5 to eliminate x:

-2y - x = -7

+

y + x = 5

----------------------------------------------------------------------------------------------------------(-2y + y) + (-x + x) = (-7 + 5)

(-y = -2) / -1

y = 2

Thus, y = 2.

Solving for x:

Now, we can solve for y by plugging in 2 for y in 2y + x = 7:

2(2) + x = 7

(4 + x = 7) - 4

x = 3

Thus, x = 3.