Questions: 2x + 3y = 12 y = 2

Transcript text: $\left\{\begin{array}{l}2 x+3 y=12 \\ y=2\end{array}\right.$

Solution

Solution Steps

Step 1: Substitute y = 2 into the first equation

Given the system of equations: \[ \begin{cases} 2x + 3y = 12 \\ y = 2 \end{cases} \] Substitute $ y = 2 $ into the first equation: \[ 2x + 3(2) = 12 \]

Step 2: Simplify and solve for x

Simplify the equation: \[ 2x + 6 = 12 \] Subtract 6 from both sides: \[ 2x = 6 \] Divide both sides by 2: \[ x = 3 \]

Step 3: Plot the solution on the graph

The solution to the system of equations is $ (x, y) = (3, 2) $. Plot this point on the graph.

Final Answer

The solution to the system of equations is $ (3, 2) $.

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