Question

Graph and check to solve the linear system. $$ \begin{aligned} &5 x+4 y=16\\\ &y=-16 \end{aligned} $$

Short answer

The solution pair for the linear system is x = 16, y = -16, graphically represented as the intersection point of the two lines.

Step-by-step solution

Substitute the value of y in Equation 1

Substitute y = -16 into the first given equation 5x + 4y = 16. This will result in 5x + 4(-16) = 16. Solve this equation to find the value of x.

Solve for x

The equation in Step 1 simplifies to 5x - 64 = 16. Add 64 to both sides to isolate the x term: 5x = 80. Lastly, divide by 5 to solve for x: x = 16.

Check the solution

Substitute x = 16 and y = -16 into the first equation to verify the solution. 5(16) + 4(-16) must equal 16, confirming that the pair of solutions is correct.

Graph the solution

Graph both equations on the Cartesian plane. The line y = -16 is a straight horizontal line across the y-axis at -16. The first equation, adjusted to y=(16-5x)/4, is a line with a slope of -5/4 and a y-intercept of 4. Both of these lines intersect at the solution point (16, -16). This graphical representation confirms the solution.