solve the system of linear equations by graphing.\n2x + 3y = 16.9\n5x = y + 7.4\nwhat is the solution to the…

Explanation:

Step1: Rewrite equations in slope - intercept form

For $2x + 3y=16.9$, solve for $y$: $3y=-2x + 16.9$, so $y=-\frac{2}{3}x+\frac{16.9}{3}\approx - 0.67x + 5.63$. For $5x=y + 7.4$, solve for $y$: $y = 5x-7.4$.

Step2: Graph the two lines

The first line $y=-0.67x + 5.63$ has a $y$-intercept of approximately $5.63$ and a slope of $-0.67$. The second line $y = 5x-7.4$ has a $y$-intercept of $-7.4$ and a slope of $5$.

Step3: Find the intersection point

We can also solve the system algebraically. Substitute $y = 5x-7.4$ into $2x+3y=16.9$: $2x+3(5x - 7.4)=16.9$. Expand: $2x+15x-22.2 = 16.9$. Combine like - terms: $17x=16.9 + 22.2$. $17x=39.1$. Solve for $x$: $x=\frac{39.1}{17}=2.3$. Substitute $x = 2.3$ into $y = 5x-7.4$: $y=5\times2.3-7.4=11.5 - 7.4 = 4.1$.

Answer:

$(2.3,4.1)$