Question

solve the linear system using substitution. your answer is an ordered pair (x, y)
y = -3x + 4
y = 4x - 10

Explanation:

Step1: Substitute \( y \) from first equation into second

We have \( y = -3x + 4 \) and \( y = 4x - 10 \). Substitute \( y \) from the first equation into the second:
\( -3x + 4 = 4x - 10 \)

Step2: Solve for \( x \)

Add \( 3x \) to both sides:
\( 4 = 7x - 10 \)
Add 10 to both sides:
\( 14 = 7x \)
Divide by 7:
\( x = 2 \)

Step3: Find \( y \) using \( x = 2 \)

Substitute \( x = 2 \) into \( y = -3x + 4 \):
\( y = -3(2) + 4 = -6 + 4 = -2 \)? Wait, no—wait, substitute into \( y = 4x - 10 \): \( y = 4(2) - 10 = 8 - 10 = -2 \)? Wait, no, wait first equation: \( y = -3(2) + 4 = -2 \). Wait, but let's check again. Wait, when \( x = 2 \), first equation: \( y = -3(2) + 4 = -2 \), second equation: \( y = 4(2) - 10 = -2 \). So ordered pair is \( (2, -2) \). Wait, but the options: the blue is (2,5), orange (5,4), cyan (2,-2), green (-2,2). So correct is (2, -2). Wait, let's recheck substitution.

Wait, original equations: \( y = -3x + 4 \) and \( y = 4x - 10 \). Set equal: \( -3x + 4 = 4x - 10 \). Add 3x: \( 4 = 7x - 10 \). Add 10: \( 14 = 7x \). \( x = 2 \). Then \( y = -3(2) + 4 = -6 + 4 = -2 \). So \( (2, -2) \).

Answer:

(2, -2)