Question

5-3 homework

1. leveled practice solve the system of equations using elimination.

2x - 7y = -13
8x - 7y = 11
multiply the second equation by
2x - 7y = -13
-8x + 7y = -11
□ + □ = □
x = □
the solution is x = □ and y = □.
8x - 7y = 11
8·(□) - 7y = 11

• 7y = 11
• 7y = □

y = □

1. solve the system of equations using elimination.

7x + 2y = -13
-7x + y = 25

1. solve the system of equations using elimination.

2x + 5y = -23
5x + 13y = -60

1. two balloons, balloon a and balloon b, have a total volume of \\(\frac{3}{5}\\) gallon. balloon a has a greater volume than balloon b. the difference of their volumes is \\(\frac{1}{5}\\) gallon. write and solve a system of equations using elimination to find the volume of each balloon.
2. reasoning suni needs to solve the system of equations using elimination.

-5x + 3y = 15
2x - 3y = -15
a. what variable should suni solve for first? explain.
b. find the solution.

Explanation:

Problem 1

Step1: Multiply eq2 by -1

$8x - 7y = 11 \implies -8x + 7y = -11$

Step2: Add eq1 and new eq2

$(2x - 7y) + (-8x + 7y) = -13 + (-11)$
$\implies -6x = -24$

Step3: Solve for x

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

Step4: Substitute x=4 into eq1

$2(4) - 7y = -13$
$\implies 8 - 7y = -13$
$\implies -7y = -21$

Step5: Solve for y

$y = \frac{-21}{-7} = 3$

Step1: Add the two equations

$(7x + 2y) + (-7x + y) = -13 + 25$
$\implies 3y = 12$

Step2: Solve for y

$y = \frac{12}{3} = 4$

Step3: Substitute y=4 into eq2

$-7x + 4 = 25$
$\implies -7x = 21$

Step4: Solve for x

$x = \frac{21}{-7} = -3$

Step1: Scale equations to eliminate x

Multiply eq1 by 5: $10x + 25y = -115$
Multiply eq2 by 2: $10x + 26y = -120$

Step2: Subtract scaled eq1 from scaled eq2

$(10x + 26y) - (10x + 25y) = -120 - (-115)$
$\implies y = -5$

Step3: Substitute y=-5 into eq1

$2x + 5(-5) = -23$
$\implies 2x -25 = -23$
$\implies 2x = 2$

Step4: Solve for x

$x = \frac{2}{2} = 1$

Answer:

$x=4$ and $y=3$

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Problem 2