Question

which points are solutions of the system of equations?
y = -2x + 7
/ select 1
y = 6x - 25

y = 3x - 7
/ select 1
y = -3x + 23

Explanation:

To solve the systems of linear equations, we can use the substitution or elimination method. Here, we'll use the substitution method by setting the two expressions for \( y \) equal to each other and solving for \( x \), then substituting \( x \) back to find \( y \).

First System: \( y = -2x + 7 \) and \( y = 6x - 25 \)

Step 1: Set the equations equal

Since both equal \( y \), we set \( -2x + 7 = 6x - 25 \).

Step 2: Solve for \( x \)

Add \( 2x \) to both sides:
\( 7 = 8x - 25 \).

Add \( 25 \) to both sides:
\( 32 = 8x \).

Divide by \( 8 \):
\( x = 4 \).

Step 3: Find \( y \)

Substitute \( x = 4 \) into \( y = -2x + 7 \):
\( y = -2(4) + 7 = -8 + 7 = -1 \).

Thus, the solution is \( (4, -1) \).

Second System: \( y = 3x - 7 \) and \( y = -3x + 23 \)

Step 1: Set the equations equal

Since both equal \( y \), we set \( 3x - 7 = -3x + 23 \).

Step 2: Solve for \( x \)

Add \( 3x \) to both sides:
\( 6x - 7 = 23 \).

Add \( 7 \) to both sides:
\( 6x = 30 \).

Divide by \( 6 \):
\( x = 5 \).

Step 3: Find \( y \)

Substitute \( x = 5 \) into \( y = 3x - 7 \):
\( y = 3(5) - 7 = 15 - 7 = 8 \).

Thus, the solution is \( (5, 8) \).

Answer:

s:

• For \( y = -2x + 7 \) and \( y = 6x - 25 \): \( (4, -1) \)
• For \( y = 3x - 7 \) and \( y = -3x + 23 \): \( (5, 8) \)