Question

Solve the following system of equations graphically on the set of axes below. y = x - 3 y = - 3/5x + 5

Answer 1

Answer:

Solution by graphing: (5, 2)

Step-by-step explanation:

y = x - 3  

y = - 3/5x + 5

To solve systems of linear equations graphically, you'll have graph each equation using 2 pairs of points.  

A great starting point is always using its intercepts:

y = x - 3

where the y-intercept is (0, -3).

To find its x-intercept, set y = 0 and solve for the value of x:

y = x - 3

0 = x - 3

Add 3 to both sides:

0 + 3 = x - 3 + 3

3 = x

Therefore, the x-intercept = (3, 0).

y = - 3/5x + 5

where the y-intercept is (0, 5).

Next, you could find a value of x that easily cancels out the fraction given by the slope (m) = -3/5. An input value of x = 5 cancels out the denominator of the slope:

y = - 3/5x + 5

y = - 3/5(5) + 5

y = -3 + 5

y = 2

Therefore, the other point that you could use to plot on the graph is (5, 2).

For y = x - 3, we'll use the line's intercepts: (0, -3) and (3, 0).  

For  y = - 3/5x + 5, we'll use (0, 5) and (5, 2).  

Plotting these points on the graph will give us a solution of (5, 2), as it is the point where both lines intersect. Attached is a screenshot of the graphed lines.

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