Question

25 multiple choice 4 points solve: $\begin{cases}2a - 3b = 5\\a + b = 10end{cases}$ (2, 8) (9, 1) (7, 3) (3, 7)

Explanation:

Step1: Isolate a in the second - equation

From $a + b=10$, we get $a = 10 - b$.

Step2: Substitute a into the first - equation

Substitute $a = 10 - b$ into $2a-3b = 5$. Then $2(10 - b)-3b=5$.
Expand the left - hand side: $20-2b-3b = 5$.
Combine like terms: $20-(2b + 3b)=5$, so $20 - 5b=5$.
Subtract 20 from both sides: $-5b=5 - 20=-15$.
Divide both sides by - 5: $b = 3$.

Step3: Find the value of a

Substitute $b = 3$ into $a = 10 - b$. Then $a=10 - 3 = 7$.

Answer:

C. $(7,3)$