Question

question 14
solve the system
3x + y = 19
x - y = 3
○ (5.5,2.5)
○ (5,3)
○ (4.5,3)
○ (5.5,5.5)

Explanation:

Step1: Add the two equations

We have the system:

$$
LATEXBLOCK0
$$

Adding the two equations to eliminate \(y\):
\((3x + y)+(x - y)=19 + 3\)
Simplify: \(3x + y+x - y=22\)
Which gives \(4x=22\)

Step2: Solve for \(x\)

Divide both sides of \(4x = 22\) by 4:
\(x=\frac{22}{4}=5.5\)

Step3: Solve for \(y\)

Substitute \(x = 5.5\) into the second equation \(x - y=3\):
\(5.5-y = 3\)
Subtract 5.5 from both sides: \(-y=3 - 5.5=-2.5\)
Multiply both sides by - 1: \(y = 2.5\)

Answer:

\((5.5,2.5)\)