Question

1. if $2x - y = 5$ and $3x + y = 10$, what is the value of $x + y$?

a. 3
b. 4
c. 5
d. 6

Explanation:

Step1: Solve for x by adding the two equations

We have the system of equations:
$$2x - y = 5$$
$$3x + y = 10$$
Adding these two equations together to eliminate \( y \):
$$(2x - y)+(3x + y)=5 + 10$$
Simplifying the left - hand side: \(2x - y+3x + y=5x\), and the right - hand side is \(15\). So we get \(5x = 15\).
Dividing both sides by 5: \(x=\frac{15}{5}=3\).

Step2: Substitute x = 3 into one of the original equations to find y

Let's substitute \(x = 3\) into the first equation \(2x-y = 5\).
We have \(2\times3-y=5\), which simplifies to \(6 - y=5\).
Subtract 6 from both sides: \(-y=5 - 6=-1\).
Multiply both sides by - 1: \(y = 1\).

Step3: Calculate x + y

Now that we know \(x = 3\) and \(y = 1\), we calculate \(x + y\):
\(x + y=3 + 1=4\).

Answer:

B. 4