QuestionSolve the system of equations: $-5y + 3z = -13$ , $4x - z = -2$ , $-7x + 9y = 5$ .

Studdy Solution

STEP 1

Assumptions1. We are given a system of three linear equations. . The system of equations is $-5y +3z = -13$ $4x - z = -$ $-7x +9y =5$ 3. We are to solve for the variables x, y, and z.

STEP 2

We can solve the system of equations by using the method of substitution or elimination. Here, we will use the method of substitution. First, we will solve the second equation for z.
$z =4x +2$

STEP 3

Substitute the expression for z from the second equation into the first and third equations.
Substituting into the first equation, we get $-5y +3(x +2) = -13$ Substituting into the third equation, we get $-7x +9y =5$

STEP 4

implify the first equation $-y +12x +6 = -13$ Rearrange to isolate y $-y = -12x -19$ Divide by - $y = \frac{12x +19}{}$

STEP 5

Substitute the expression for y from the first equation into the third equation $-7x +9\left(\frac{12x +19}{5}\right) =5$

STEP 6

implify the third equation $-x + \frac{108x +171}{5} =5$ Multiply through by5 to clear the fraction $-35x +108x +171 =25$

STEP 7

Combine like terms $73x +171 =25$ Subtract171 from both sides $73x = -146$ Divide by73 $x = -2$

STEP 8

Substitute x = -2 into the equation for y $y = \frac{12(-2) +19}{5}$ implify to find the value of y $y = -1$

STEP 9

Substitute x = -2 into the equation for z $z =4(-2) +2$ implify to find the value of z $z = -6$ The solution to the system of equations is x = -2, y = -, z = -6.

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QuestionSolve the system of equations: $-5y + 3z = -13$ , $4x - z = -2$ , $-7x + 9y = 5$ .

Studdy Solution

STEP 1

Assumptions1. We are given a system of three linear equations. . The system of equations is $-5y +3z = -13$ $4x - z = -$ $-7x +9y =5$ 3. We are to solve for the variables x, y, and z.

STEP 2

We can solve the system of equations by using the method of substitution or elimination. Here, we will use the method of substitution. First, we will solve the second equation for z.
$z =4x +2$

STEP 3

Substitute the expression for z from the second equation into the first and third equations.
Substituting into the first equation, we get $-5y +3(x +2) = -13$ Substituting into the third equation, we get $-7x +9y =5$

STEP 4

implify the first equation $-y +12x +6 = -13$ Rearrange to isolate y $-y = -12x -19$ Divide by - $y = \frac{12x +19}{}$

STEP 5

Substitute the expression for y from the first equation into the third equation $-7x +9\left(\frac{12x +19}{5}\right) =5$

STEP 6

implify the third equation $-x + \frac{108x +171}{5} =5$ Multiply through by5 to clear the fraction $-35x +108x +171 =25$

STEP 7

Combine like terms $73x +171 =25$ Subtract171 from both sides $73x = -146$ Divide by73 $x = -2$

STEP 8

Substitute x = -2 into the equation for y $y = \frac{12(-2) +19}{5}$ implify to find the value of y $y = -1$

STEP 9

Substitute x = -2 into the equation for z $z =4(-2) +2$ implify to find the value of z $z = -6$ The solution to the system of equations is x = -2, y = -, z = -6.

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QuestionSolve the system of equations: −5y+3z=−13-5y + 3z = -13−5y+3z=−13, 4x−z=−24x - z = -24x−z=−2, −7x+9y=5-7x + 9y = 5−7x+9y=5.

Studdy Solution

STEP 1

Assumptions1. We are given a system of three linear equations. . The system of equations is −5y+3z=−13-5y +3z = -13−5y+3z=−13 4x−z=−4x - z = -4x−z=− −7x+9y=5-7x +9y =5−7x+9y=53. We are to solve for the variables x, y, and z.

STEP 2

We can solve the system of equations by using the method of substitution or elimination. Here, we will use the method of substitution. First, we will solve the second equation for z.z=4x+2z =4x +2z=4x+2

STEP 3

Substitute the expression for z from the second equation into the first and third equations.Substituting into the first equation, we get−5y+3(x+2)=−13-5y +3(x +2) = -13−5y+3(x+2)=−13Substituting into the third equation, we get−7x+9y=5-7x +9y =5−7x+9y=5

STEP 4

implify the first equation−y+12x+6=−13-y +12x +6 = -13−y+12x+6=−13Rearrange to isolate y−y=−12x−19-y = -12x -19−y=−12x−19Divide by -y=12x+19y = \frac{12x +19}{}y=12x+19​

STEP 5

Substitute the expression for y from the first equation into the third equation−7x+9(12x+195)=5-7x +9\left(\frac{12x +19}{5}\right) =5−7x+9(512x+19​)=5

STEP 6

implify the third equation−x+108x+1715=5-x + \frac{108x +171}{5} =5−x+5108x+171​=5Multiply through by5 to clear the fraction−35x+108x+171=25-35x +108x +171 =25−35x+108x+171=25

STEP 7

Combine like terms73x+171=2573x +171 =2573x+171=25Subtract171 from both sides73x=−14673x = -14673x=−146Divide by73x=−2x = -2x=−2

STEP 8

Substitute x = -2 into the equation for yy=12(−2)+195y = \frac{12(-2) +19}{5}y=512(−2)+19​implify to find the value of yy=−1y = -1y=−1

STEP 9

Substitute x = -2 into the equation for zz=4(−2)+2z =4(-2) +2z=4(−2)+2implify to find the value of zz=−6z = -6z=−6The solution to the system of equations is x = -2, y = -, z = -6.

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QuestionSolve the system of equations: $-5y + 3z = -13$ , $4x - z = -2$ , $-7x + 9y = 5$ .

Assumptions1. We are given a system of three linear equations. . The system of equations is $-5y +3z = -13$ $4x - z = -$ $-7x +9y =5$ 3. We are to solve for the variables x, y, and z.

We can solve the system of equations by using the method of substitution or elimination. Here, we will use the method of substitution. First, we will solve the second equation for z.
$z =4x +2$

Substitute the expression for z from the second equation into the first and third equations.
Substituting into the first equation, we get $-5y +3(x +2) = -13$ Substituting into the third equation, we get $-7x +9y =5$

implify the first equation $-y +12x +6 = -13$ Rearrange to isolate y $-y = -12x -19$ Divide by - $y = \frac{12x +19}{}$

Substitute the expression for y from the first equation into the third equation $-7x +9\left(\frac{12x +19}{5}\right) =5$

implify the third equation $-x + \frac{108x +171}{5} =5$ Multiply through by5 to clear the fraction $-35x +108x +171 =25$

Combine like terms $73x +171 =25$ Subtract171 from both sides $73x = -146$ Divide by73 $x = -2$

Substitute x = -2 into the equation for y $y = \frac{12(-2) +19}{5}$ implify to find the value of y $y = -1$

Substitute x = -2 into the equation for z $z =4(-2) +2$ implify to find the value of z $z = -6$ The solution to the system of equations is x = -2, y = -, z = -6.