Question

algebra 1
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name ana ramirll
lesson 7.2 day 2 assignment \t\t\t\t\t\t\t\t\t\t\t\tdate 11/7/24
solve each system by substitution.

1. $3x - 4y = 16$

$y = 2$

1. $2x - y = 7$

$y = 2x - 7$

1. $2x + y = -18$

$-10x + 5y = 10$

1. $3x + 6y = -9$

$x + 2y = -2$

Explanation:

Problem 1:

Step1: Substitute \( y = 2 \) into \( 3x - 4y = 16 \)

\( 3x - 4(2) = 16 \)

Step2: Simplify and solve for \( x \)

\( 3x - 8 = 16 \)
\( 3x = 16 + 8 \)
\( 3x = 24 \)
\( x = \frac{24}{3} = 8 \)

Step1: Substitute \( y = 2x - 7 \) into \( 2x - y = 7 \)

\( 2x - (2x - 7) = 7 \)

Step2: Simplify the equation

\( 2x - 2x + 7 = 7 \)
\( 7 = 7 \)
This is an identity, so there are infinitely many solutions (the two lines are coincident).

Step1: Solve \( 2x + y = -18 \) for \( y \)

\( y = -2x - 18 \)

Step2: Substitute \( y = -2x - 18 \) into \( -10x + 5y = 10 \)

\( -10x + 5(-2x - 18) = 10 \)

Step3: Simplify and solve for \( x \)

\( -10x - 10x - 90 = 10 \)
\( -20x - 90 = 10 \)
\( -20x = 10 + 90 \)
\( -20x = 100 \)
\( x = \frac{100}{-20} = -5 \)

Step4: Substitute \( x = -5 \) into \( y = -2x - 18 \)

\( y = -2(-5) - 18 \)
\( y = 10 - 18 \)
\( y = -8 \)

Answer:

The solution is \( x = 8, y = 2 \) (or \( (8, 2) \))

Problem 2: