Questions: What is the value of the y-coordinate of the solution to the system of equations 2x+y=8 and x-3y=-3 -3 3 2 -2

Transcript text: Multiple Choice 2 points What is the value of the $y$-coordinate of the solution to the system of equations $2 x+y=8$ and $x-3 y=-3$ $-3$ 3 2 -2

Solution

Solution Steps

Step 1: Solve one of the equations for one variable

We will solve the first equation $ 2x + y = 8 $ for $ y $: \[ y = 8 - 2x \]

Step 2: Substitute the expression into the second equation

Substitute $ y = 8 - 2x $ into the second equation $ x - 3y = -3 $: \[ x - 3(8 - 2x) = -3 \]

Step 3: Simplify and solve for $ x $

Expand and simplify the equation: \[ x - 24 + 6x = -3 \] \[ 7x - 24 = -3 \] \[ 7x = 21 \] \[ x = 3 \]

Step 4: Substitute $ x = 3 $ back into the expression for $ y $

Substitute $ x = 3 $ into $ y = 8 - 2x $: \[ y = 8 - 2(3) \] \[ y = 8 - 6 \] \[ y = 2 \]

The value of the $ y $-coordinate is $ 2 $.

Final Answer

$\boxed{2}$

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