Math  /  Algebra

QuestionSolve the system of equations by graphing. {x+y=9xy=5\left\{\begin{array}{l} x+y=9 \\ x-y=5 \end{array}\right.
Use the graphing tool to graph the system. \qquad

Studdy Solution

STEP 1

1. The system of linear equations involves two variables, xx and yy.
2. Each equation represents a straight line in the Cartesian plane.
3. The solution to the system is the point where the two lines intersect.

STEP 2

1. Rewrite each equation in slope-intercept form (y=mx+by = mx + b).
2. Graph both equations on the Cartesian plane.
3. Identify the point of intersection of the two lines.
4. Verify the solution by substituting the coordinates of the intersection point back into the original equations.

STEP 3

Rewrite the first equation, x+y=9x + y = 9, in slope-intercept form.
y=9xy = 9 - x

STEP 4

Rewrite the second equation, xy=5x - y = 5, in slope-intercept form.
y=x5y = x - 5

STEP 5

Graph the first equation y=9xy = 9 - x.
This line has a slope of 1-1 and a y-intercept of 99.

STEP 6

Graph the second equation y=x5y = x - 5.
This line has a slope of 11 and a y-intercept of 5-5.

STEP 7

Identify the point of intersection between the two lines.
By looking at the graphs of the lines y=9xy = 9 - x and y=x5y = x - 5, we find that they intersect at the point (7,2)(7, 2).

STEP 8

Verify the solution by substituting x=7x = 7 and y=2y = 2 back into the original equations.
First equation: 7+2=9(True)7 + 2 = 9 \quad \text{(True)}
Second equation: 72=5(True)7 - 2 = 5 \quad \text{(True)}
Both equations are satisfied.
Solution: The solution to the system of equations is (7,2)(7, 2).

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