The task in the image is asking to determine which point from the specified set satisfies each system of equations.

Here is the first system:

$y = 2x - 9$ $y = -4x + 3$

Given the points: (2, -5), (-3, -15), and (1, -1), you need to check which of these points satisfies both equations.

Steps for solution:

1. Substitute the x and y values of each point into both equations to check for consistency.

For point (2, -5):

Substitute x = 2 and y = -5 into both equations:

• For $y = 2x - 9$: $-5 = 2(2) - 9 \implies -5 = 4 - 9 \implies -5 = -5 \quad \text{(True)}$

• For $y = -4x + 3$: $-5 = -4(2) + 3 \implies -5 = -8 + 3 \implies -5 = -5 \quad \text{(True)}$ So, (2, -5) satisfies both equations.

For point (-3, -15):

Substitute x = -3 and y = -15 into both equations:

• For $y = 2x - 9$: $-15 = 2(-3) - 9 \implies -15 = -6 - 9 \implies -15 = -15 \quad \text{(True)}$

• For $y = -4x + 3$: $-15 = -4(-3) + 3 \implies -15 = 12 + 3 \implies -15 = 15 \quad \text{(False)}$ So, (-3, -15) does not satisfy the second equation.

For point (1, -1):

Substitute x = 1 and y = -1 into both equations:

• For $y = 2x - 9$: $-1 = 2(1) - 9 \implies -1 = 2 - 9 \implies -1 = -7 \quad \text{(False)}$

• For $y = -4x + 3$: $-1 = -4(1) + 3 \implies -1 = -4 + 3 \implies -1 = -1 \quad \text{(True)}$ So, (1, -1) does not satisfy the first equation.

Conclusion:

The point (2, -5) satisfies both equations.

Would you like further details or have any questions about the solution?

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Tip: When solving systems of linear equations, always check the validity of each point by substituting into both equations to confirm if they satisfy the system.