Problem

Solve the following system of equations graphically on the set of axes below. \[ \begin{array}{l} y=-x+7 \\ 2 x-y=8 \end{array} \] Plot two lines by clicking the graph. Click a line to delete it.

Solution

Step 1 :First, we rewrite the second equation in the form of y = mx + b, which is the standard form of a linear equation. We get \(y = 2x - 8\).

Step 2 :Now we have two equations: \(y = -x + 7\) and \(y = 2x - 8\).

Step 3 :We can find the solution by setting these two equations equal to each other and solving for x: \(-x + 7 = 2x - 8\).

Step 4 :Adding x to both sides, we get \(7 = 3x - 8\).

Step 5 :Adding 8 to both sides, we get \(15 = 3x\).

Step 6 :Dividing both sides by 3, we get \(x = 5\).

Step 7 :Substituting x = 5 into the first equation, we get \(y = -5 + 7 = 2\).

Step 8 :Thus, the solution to the system of equations is \(\boxed{(5,2)}\).

Step 9 :We can check this solution by substituting x = 5 and y = 2 into the second equation: \(2*5 - 2 = 8\), which is true. So, the solution is correct.

From Solvely APP
Source: https://solvelyapp.com/problems/8130/

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