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.\\((\quad,\quad)\\)

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(2x + 3y=16.9\), 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 \(5x=y + 7.4\), solve for \(y\):
Subtract 7.4 from both sides: \(y = 5x-7.4\)

Step2: Find the intersection point (graphically or by substitution)

We can use substitution. Substitute \(y = 5x - 7.4\) into the first equation:
\(2x+3(5x - 7.4)=16.9\)
Expand the left - hand side: \(2x+15x-22.2 = 16.9\)
Combine like terms: \(17x-22.2 = 16.9\)
Add 22.2 to both sides: \(17x=16.9 + 22.2=39.1\)
Divide both sides 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:

\((2.3, 4.1)\)