Question

1. $-4x - 15y = -17$ $-x + 5y = -13$ $(8, -1)$ 8. $-x - 7y = 14$ $-4x - 14y = 28$ $(0, -2)$ 9. $-x - 9y = 15$ $-7x - 9y = -3$ $(3, -2)$ 10. $7x - 2y = 3$ $4x - 2y = -6$ $(3, 9)$

Explanation:

Let's solve each system of linear equations step by step.

Problem 7:

System:

$$
LATEXBLOCK0
$$

Step 1: Solve the second equation for \(x\)

From \(-x + 5y = -13\), we get \(x = 5y + 13\).

Step 2: Substitute \(x = 5y + 13\) into the first equation

$$
LATEXBLOCK1
$$

Step 3: Substitute \(y = -1\) back into \(x = 5y + 13\)

$$ x = 5(-1) + 13 = -5 + 13 = 8 $$

So the solution is \((8, -1)\), which matches the given answer.

Problem 8:

System:

$$
LATEXBLOCK2
$$

Step 1: Simplify the equations

From the first equation, \(x = -7y - 14\).

Step 2: Substitute \(x = -7y - 14\) into the second equation

$$
LATEXBLOCK3
$$

Step 3: Substitute \(y = -2\) back into \(x = -7y - 14\)

$$ x = -7(-2) - 14 = 14 - 14 = 0 $$

So the solution is \((0, -2)\), which matches the given answer.

Problem 9:

System:

$$
LATEXBLOCK4
$$

Step 1: Subtract the first equation from the second equation

$$
LATEXBLOCK5
$$

Step 2: Substitute \(x = 3\) into the first equation

$$
LATEXBLOCK6
$$

So the solution is \((3, -2)\), which matches the given answer.

Problem 10:

System:

$$
LATEXBLOCK7
$$

Step 1: Subtract the second equation from the first equation

$$
LATEXBLOCK8
$$

Step 2: Substitute \(x = 3\) into the first equation

$$
LATEXBLOCK9
$$

So the solution is \((3, 9)\), which matches the given answer.

Answer:

Let's solve each system of linear equations step by step.

Problem 7:

System:

$$
LATEXBLOCK0
$$

Step 1: Solve the second equation for \(x\)

From \(-x + 5y = -13\), we get \(x = 5y + 13\).

Step 2: Substitute \(x = 5y + 13\) into the first equation

$$
LATEXBLOCK1
$$

Step 3: Substitute \(y = -1\) back into \(x = 5y + 13\)

$$ x = 5(-1) + 13 = -5 + 13 = 8 $$

So the solution is \((8, -1)\), which matches the given answer.

Problem 8:

System:

$$
LATEXBLOCK2
$$

Step 1: Simplify the equations

From the first equation, \(x = -7y - 14\).

Step 2: Substitute \(x = -7y - 14\) into the second equation

$$
LATEXBLOCK3
$$

Step 3: Substitute \(y = -2\) back into \(x = -7y - 14\)

$$ x = -7(-2) - 14 = 14 - 14 = 0 $$

So the solution is \((0, -2)\), which matches the given answer.

Problem 9:

System:

$$
LATEXBLOCK4
$$

Step 1: Subtract the first equation from the second equation

$$
LATEXBLOCK5
$$

Step 2: Substitute \(x = 3\) into the first equation

$$
LATEXBLOCK6
$$

So the solution is \((3, -2)\), which matches the given answer.

Problem 10:

System:

$$
LATEXBLOCK7
$$

Step 1: Subtract the second equation from the first equation

$$
LATEXBLOCK8
$$

Step 2: Substitute \(x = 3\) into the first equation

$$
LATEXBLOCK9
$$

So the solution is \((3, 9)\), which matches the given answer.