Solve the following system of equations graphically on the set of axes below.y, equals, minus, x, plus, 2y=−x+22, x, minus, y, equals, 72x−y=7

1. Break Down the Problem

To solve the system of equations graphically, we need to rewrite each equation in slope-intercept form (y = mx + b) so we can plot them on a graph.

2. Relevant Concepts

The given equations:

1. $y = -x + 22$
2. $x - y = 7$

3. Analysis and Detail

We will convert the second equation into slope-intercept form.

Equation 2: $x - y = 7 \implies -y = -x + 7 \implies y = x - 7$

Now we have the two equations:

1. $y = -x + 22$
2. $y = x - 7$

4. Verify and Summarize

To graphically solve, we will determine the points of intersection of the two lines:

• For $y = -x + 22$:

  • When $x = 0, y = 22$
  • When $x = 22, y = 0$

• For $y = x - 7$:

  • When $x = 0, y = -7$
  • When $x = 7, y = 0$

Graphical Representation (for drawing the lines)

• The first line intersects $y$-axis at (0, 22) and $x$-axis at (22, 0).
• The second line intersects $y$-axis at (0, -7) and $x$-axis at (7, 0).

Plot these points on set axes and draw the lines for each equation.

Final Answer

The solution to the system of equations can be viewed as the point where the two lines intersect on the graph. The coordinates of this intersection point are the solution to the system.

Let us find the intersection algebraically for clarity: Set the equations equal to each other: $-x + 22 = x - 7$ $22 + 7 = 2x \implies 29 = 2x \implies x = \frac{29}{2} = 14.5$ Substituting $x = 14.5$ back into one of the equations to find $y$: $y = -14.5 + 22 = 7.5$

Thus, the final solution (intersection point) is: $\boxed{(14.5, 7.5)}$