Math / Algebra

QuestionFind the solution to the system of linear equations using substitution. $\left\{\begin{array}{l} x=9 y+20 \\ x=-8 y-14 \end{array}\right.$
Enter the system's solution as an ordered pair. If the system has no solution, enter "none". If the system has infinitely many solutions, enter "infinitely many solutions".
Solution: $\square$

Studdy Solution

STEP 1

1. We are given a system of two linear equations.
2. The goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.
3. We will use the substitution method to solve the system.

STEP 2

1. Set the equations equal to each other since both are solved for $x$ .
2. Solve for $y$ .
3. Substitute the value of $y$ back into one of the original equations to find $x$ .
4. Write the solution as an ordered pair.
5. Verify the solution by checking both original equations.

STEP 3

Since both equations are solved for $x$ , we can set them equal to each other:
$9y + 20 = -8y - 14$

STEP 4

Solve for $y$ by first adding $8y$ to both sides:
$9y + 8y + 20 = -14$
Combine like terms:
$17y + 20 = -14$
Subtract 20 from both sides:
$17y = -34$
Divide both sides by 17:
$y = -2$

STEP 5

Substitute $y = -2$ back into one of the original equations to find $x$ . We'll use the first equation:
$x = 9(-2) + 20$
Calculate:
$x = -18 + 20$
$x = 2$

STEP 6

The solution to the system is the ordered pair:
$(x, y) = (2, -2)$

STEP 7

Verify the solution by substituting $x = 2$ and $y = -2$ into the second equation:
$x = -8(-2) - 14$
Calculate:
$2 = 16 - 14$
$2 = 2$
Both equations are satisfied, confirming the solution.
Solution: $(2, -2)$

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Studdy Solution

STEP 1

1. We are given a system of two linear equations.
2. The goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.
3. We will use the substitution method to solve the system.

STEP 2

1. Set the equations equal to each other since both are solved for $x$ .
2. Solve for $y$ .
3. Substitute the value of $y$ back into one of the original equations to find $x$ .
4. Write the solution as an ordered pair.
5. Verify the solution by checking both original equations.

STEP 3

Since both equations are solved for $x$ , we can set them equal to each other:
$9y + 20 = -8y - 14$

STEP 4

Solve for $y$ by first adding $8y$ to both sides:
$9y + 8y + 20 = -14$
Combine like terms:
$17y + 20 = -14$
Subtract 20 from both sides:
$17y = -34$
Divide both sides by 17:
$y = -2$

STEP 5

Substitute $y = -2$ back into one of the original equations to find $x$ . We'll use the first equation:
$x = 9(-2) + 20$
Calculate:
$x = -18 + 20$
$x = 2$

STEP 6

The solution to the system is the ordered pair:
$(x, y) = (2, -2)$

STEP 7

Verify the solution by substituting $x = 2$ and $y = -2$ into the second equation:
$x = -8(-2) - 14$
Calculate:
$2 = 16 - 14$
$2 = 2$
Both equations are satisfied, confirming the solution.
Solution: $(2, -2)$

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Studdy Solution

STEP 1

1. We are given a system of two linear equations.2. The goal is to find the values of x x x and y y y that satisfy both equations simultaneously.3. We will use the substitution method to solve the system.

STEP 2

1. Set the equations equal to each other since both are solved for x x x.2. Solve for y y y.3. Substitute the value of y y y back into one of the original equations to find x x x.4. Write the solution as an ordered pair.5. Verify the solution by checking both original equations.

STEP 3

Since both equations are solved for x x x, we can set them equal to each other:9y+20=−8y−14 9y + 20 = -8y - 14 9y+20=−8y−14

STEP 4

Solve for y y y by first adding 8y 8y 8y to both sides:9y+8y+20=−14 9y + 8y + 20 = -14 9y+8y+20=−14Combine like terms:17y+20=−14 17y + 20 = -14 17y+20=−14Subtract 20 from both sides:17y=−34 17y = -34 17y=−34Divide both sides by 17:y=−2 y = -2 y=−2

STEP 5

Substitute y=−2 y = -2 y=−2 back into one of the original equations to find x x x. We'll use the first equation:x=9(−2)+20 x = 9(-2) + 20 x=9(−2)+20Calculate:x=−18+20 x = -18 + 20 x=−18+20x=2 x = 2 x=2

STEP 6

The solution to the system is the ordered pair:(x,y)=(2,−2) (x, y) = (2, -2) (x,y)=(2,−2)

STEP 7

Verify the solution by substituting x=2 x = 2 x=2 and y=−2 y = -2 y=−2 into the second equation:x=−8(−2)−14 x = -8(-2) - 14 x=−8(−2)−14Calculate:2=16−14 2 = 16 - 14 2=16−142=2 2 = 2 2=2Both equations are satisfied, confirming the solution. Solution: (2,−2)(2, -2)(2,−2)

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1. We are given a system of two linear equations.
2. The goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.
3. We will use the substitution method to solve the system.

1. Set the equations equal to each other since both are solved for $x$ .
2. Solve for $y$ .
3. Substitute the value of $y$ back into one of the original equations to find $x$ .
4. Write the solution as an ordered pair.
5. Verify the solution by checking both original equations.

Since both equations are solved for $x$ , we can set them equal to each other:
$9y + 20 = -8y - 14$

Solve for $y$ by first adding $8y$ to both sides:
$9y + 8y + 20 = -14$
Combine like terms:
$17y + 20 = -14$
Subtract 20 from both sides:
$17y = -34$
Divide both sides by 17:
$y = -2$

Substitute $y = -2$ back into one of the original equations to find $x$ . We'll use the first equation:
$x = 9(-2) + 20$
Calculate:
$x = -18 + 20$
$x = 2$

The solution to the system is the ordered pair:
$(x, y) = (2, -2)$

Verify the solution by substituting $x = 2$ and $y = -2$ into the second equation:
$x = -8(-2) - 14$
Calculate:
$2 = 16 - 14$
$2 = 2$
Both equations are satisfied, confirming the solution.
Solution: $(2, -2)$