Question

The equations (9x - 10y = 6), (8x - 10y = -23), (9x + 10y = -16), and (8x + 10y = 13) are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (-2, 0.75) and (-2, 1.5). Blue line goes through (-1.75, 0) and (1, -2). Pink line goes through (-1.5, -2), and (1.5, 0.75). Purple line goes through (0, 1.25) and (1, 0.5). Which is the approximate solution for the system of equations (8x - 10y = -23) and (9x + 10y = -16)?

a) (-2.3, 0.5)
b) (-2.5, 1)
c) (-2.3, -0.5)
d) (-2.5, -1)

Answer 1

To solve for the system of equations (8x - 10y = -23) and (9x + 10y = -16), we add the equations to eliminate the y-term and solve for x. Then, we substitute x back into one of the equations to find y. The approximate solution is (-2.3, 0.5).

Step-by-step explanation:

The student is trying to solve a system of two linear equations, namely (8x - 10y = -23) and (9x + 10y = -16). To find the approximate solution for this system, we can add these two equations together, which will eliminate the y-term, allowing us to solve for x. Once we have solved for x, we can substitute the value of x into either of the original equations to find the corresponding y-value.

The addition of the two equations gives us:

• 8x - 10y + 9x + 10y = -23 - 16
• 17x = -39
• x = -39 / 17
• x = -2.294

Approximating x to one decimal place gives us x = -2.3. To find y, we substitute x back into the first original equation:

• 8(-2.3) - 10y = -23
• -18.4 - 10y = -23
• -10y = -23 + 18.4
• -10y = -4.6
• y = -4.6 / -10
• y = 0.46

Approximating y to one decimal place gives us y = 0.5. Therefore, the approximate solution for the system is x = -2.3 and y = 0.5, which corresponds to option a) (-2.3, 0.5).