Question

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Explanation:

Problem 2

Step1: Substitute $y$ into second equation

$-x + 3(-2x + 4) = -9$

Step2: Simplify and solve for $x$

$-x -6x +12 = -9 \\
-7x = -21 \\
x = 3$

Step3: Substitute $x$ to find $y$

$y = -2(3) + 4 = -6 + 4 = -2$

Problem 3

Step1: Isolate $y$ from first equation

$y = 4 - 3x$

Step2: Set equal to second equation

$4 - 3x = 4x - 10$

Step3: Solve for $x$

$4 + 10 = 4x + 3x \\
14 = 7x \\
x = 2$

Step4: Substitute $x$ to find $y$

$y = 4 - 3(2) = 4 - 6 = -2$

Problem 4

Step1: Substitute $y$ into second equation

$2x + 2(5x - 4) = 16$

Step2: Simplify and solve for $x$

$2x + 10x - 8 = 16 \\
12x = 24 \\
x = 2$

Step3: Substitute $x$ to find $y$

$y = 5(2) - 4 = 10 - 4 = 6$

Problem 5

Step1: Substitute $y$ into second equation

$3x - 8(5x - 3) = 24$

Step2: Simplify and solve for $x$

$3x - 40x + 24 = 24 \\
-37x = 0 \\
x = 0$

Step3: Substitute $x$ to find $y$

$y = 5(0) - 3 = -3$

Answer:

Problem 2: $x=3$, $y=-2$
Problem 3: $x=2$, $y=-2$
Problem 4: $x=2$, $y=6$
Problem 5: $x=0$, $y=-3$