Question

geometry with statistics honors geometry readiness assessment solve the system of equations 2a + 3b = 23 3a - 2b = 2 a a = -4, b = -7 b a = 10, b = 1 c a = 4, b = 5 d no solution

Explanation:

Step1: Multiply equations for elimination

Multiply the first - equation $2a + 3b=23$ by 2 and the second - equation $3a−2b = 2$ by 3.
The first equation becomes $4a + 6b=46$ (since $2(2a + 3b)=2\times23$), and the second equation becomes $9a-6b = 6$ (since $3(3a - 2b)=3\times2$).

Step2: Add the two new equations

Add $4a + 6b=46$ and $9a-6b = 6$ together.
$(4a+9a)+(6b - 6b)=46 + 6$.
$13a=52$.

Step3: Solve for $a$

Divide both sides of $13a = 52$ by 13.
$a=\frac{52}{13}=4$.

Step4: Substitute $a = 4$ into the first original equation

Substitute $a = 4$ into $2a+3b = 23$.
$2\times4+3b=23$.
$8 + 3b=23$.

Step5: Solve for $b$

Subtract 8 from both sides: $3b=23 - 8=15$.
Divide both sides by 3: $b = 5$.

Answer:

C. $a = 4,b = 5$