Question

in exercises 1–8, solve the system by elimination. check your solution. example 1 1. $x + 2y = 13$ $-x + y = 5$ 2. $9x + y = 2$ $-4x - y = -17$ 3. $5x + 6y = 50$ $x - 6y = -26$ 4. $-x + y = 4$ $x + 3y = 4$ 5. $-3x - 5y = -7$ $-4x + 5y = 14$ 6. $1.5x - 9y = -21$ $-1.5x - 3y = 9$ 7. $-y - 10 = 6x$ $5x + y = -10$ 8. $3x - 30 = y$ $7y - 6 = 3x$

Explanation:

For Problem 3

Step1: Add the two equations

$$(5x + 6y) + (x - 6y) = 50 + (-26)$$
Simplify: $6x = 24$

Step2: Solve for $x$

$$x = \frac{24}{6} = 4$$

Step3: Substitute $x=4$ into second equation

$$4 - 6y = -26$$

Step4: Solve for $y$

$$-6y = -26 - 4 = -30$$
$$y = \frac{-30}{-6} = 5$$

Step5: Verify solution

Substitute $x=4,y=5$ into first equation: $5(4)+6(5)=20+30=50$ (matches)
Substitute into second equation: $4-6(5)=4-30=-26$ (matches)

Step1: Add the two equations

$$(x + 2y) + (-x + y) = 13 + 5$$
Simplify: $3y = 18$

Step2: Solve for $y$

$$y = \frac{18}{3} = 6$$

Step3: Substitute $y=6$ into second equation

$$-x + 6 = 5$$

Step4: Solve for $x$

$$-x = 5 - 6 = -1$$
$$x = 1$$

Step5: Verify solution

Substitute $x=1,y=6$ into first equation: $1+2(6)=1+12=13$ (matches)
Substitute into second equation: $-1+6=5$ (matches)

Step1: Add the two equations

$$(9x + y) + (-4x - y) = 2 + (-17)$$
Simplify: $5x = -15$

Step2: Solve for $x$

$$x = \frac{-15}{5} = -3$$

Step3: Substitute $x=-3$ into first equation

$$9(-3) + y = 2$$

Step4: Solve for $y$

$$-27 + y = 2$$
$$y = 2 + 27 = 29$$

Step5: Verify solution

Substitute $x=-3,y=29$ into first equation: $9(-3)+29=-27+29=2$ (matches)
Substitute into second equation: $-4(-3)-29=12-29=-17$ (matches)

Answer:

$x=4$, $y=5$

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For Problem 1