Question

solve the system of linear equations by graphing.
2x + 3y = 16.9
5x = y + 7.4

what is the solution to the system of linear equations? round to the nearest tenth as needed.
( , )

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(2x + 3y=16.9\), we solve for \(y\):
Subtract \(2x\) from both sides: \(3y=-2x + 16.9\)
Divide by 3: \(y =-\frac{2}{3}x+\frac{16.9}{3}\approx-\frac{2}{3}x + 5.63\)

For the second equation \(5x=y + 7.4\), we solve for \(y\):
Subtract 7.4 from both sides: \(y = 5x-7.4\)

Step2: Find the intersection point (solve the system algebraically to check)

Set the two expressions for \(y\) equal to each other:
\(-\frac{2}{3}x+\frac{16.9}{3}=5x - 7.4\)
Multiply through by 3 to clear the fraction:
\(- 2x+16.9 = 15x-22.2\)
Add \(2x\) to both sides:
\(16.9=17x - 22.2\)
Add 22.2 to both sides:
\(16.9 + 22.2=17x\)
\(39.1 = 17x\)
Divide by 17: \(x=\frac{39.1}{17}\approx2.3\)

Step3: Find the value of \(y\)

Substitute \(x = 2.3\) into \(y = 5x-7.4\)
\(y=5\times2.3-7.4=11.5 - 7.4 = 4.1\)

Answer:

\((2.3, 4.1)\)