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QuestionSolve the system: 3x+6y=363x + 6y = 36 and 15x−6y=−7215x - 6y = -72. What is xx?

Studdy Solution

STEP 1

Assumptions1. We have two linear equations in two variables, x and y. . The equations are3x +6y =3615x -6y = -72

STEP 2

The given problem is a system of linear equations. We can solve this system by adding the two equations together. This is possible because the coefficients of y in both equations are equal in magnitude but opposite in sign, so they will cancel each other out when added.
x+6y+15x−6y=36−72x +6y +15x -6y =36 -72

STEP 3

implify the left side of the equation by combining like terms.
18x=36−7218x =36 -72

STEP 4

implify the right side of the equation.
18x=−3618x = -36

STEP 5

To solve for x, we need to isolate x. We can do this by dividing both sides of the equation by the coefficient of x, which is18.
x=−3618x = \frac{-36}{18}

STEP 6

Calculate the value of x.
x=−3618=−2x = \frac{-36}{18} = -2So, the solution to the system of equations is x = -2. To find the value of y, we can substitute x = -2 into either of the original equations. Let's use the first equation3x +6y =36.

STEP 7

Substitute x = -2 into the first equation.
3(−2)+6y=363(-2) +6y =36

STEP 8

implify the left side of the equation.
−6+6y=36-6 +6y =36

STEP 9

To isolate y, add6 to both sides of the equation.
6y=36+66y =36 +6

STEP 10

implify the right side of the equation.
6y=426y =42

STEP 11

To solve for y, divide both sides of the equation by the coefficient of y, which is6.
y=426y = \frac{42}{6}

STEP 12

Calculate the value of y.
y=426=7y = \frac{42}{6} =7So, the solution to the system of equations is x = -2 and y =7.

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