Question

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what is the solution of the system of equations? use a graphing utility. round your answers to the thousandths, if necessary.

1. ( y = -\frac{1}{2}x + 3 )

( y = 6x - 5 )
a. ( (3.25, 10.25) )
b. ( (1.231, 2.385) )
c. ( (2.076, 4.378) )
d. ( (-2.340, -5.702) )

Explanation:

Step1: Set equations equal

Since \( y = -\frac{1}{2}x + 3 \) and \( y = 6x - 5 \), set them equal: \( -\frac{1}{2}x + 3 = 6x - 5 \)

Step2: Solve for x

Add \( \frac{1}{2}x \) to both sides: \( 3 = 6x + \frac{1}{2}x - 5 \)
Combine like terms: \( 3 = \frac{13}{2}x - 5 \)
Add 5 to both sides: \( 8 = \frac{13}{2}x \)
Multiply both sides by \( \frac{2}{13} \): \( x = \frac{16}{13} \approx 1.231 \)

Step3: Find y

Substitute \( x \approx 1.231 \) into \( y = 6x - 5 \):
\( y = 6(1.231) - 5 = 7.386 - 5 = 2.386 \approx 2.385 \) (matches option b)

Answer:

b. (1.231,2.385)