Question

a system of equations is shown
\\(\

$$\begin{cases}y = \\frac{2}{3}x - 1\\\\y = \\frac{1}{2}x + 2\\end{cases}$$

\\)
which ordered pair represents a solution to the system of equations?
a (12,?)
b (0, - 1)
c (18, 11)
d (6, 5)

Explanation:

Step1: Set the two equations equal

Since $y = \frac{2}{3}x - 1$ and $y=\frac{1}{2}x + 2$, we set $\frac{2}{3}x-1=\frac{1}{2}x + 2$.

Step2: Get a common - denominator

Multiply through by 6 to clear the fractions: $6\times(\frac{2}{3}x-1)=6\times(\frac{1}{2}x + 2)$. This gives $4x-6 = 3x+12$.

Step3: Solve for x

Subtract $3x$ from both sides: $4x-3x-6=3x - 3x+12$, so $x = 18$.

Step4: Solve for y

Substitute $x = 18$ into $y=\frac{1}{2}x + 2$. Then $y=\frac{1}{2}\times18+2=9 + 2=11$.

Answer:

C. (18, 11)