Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for x,y, and z {:[x+6y-z=-5],[-2x-5y+2z=3],[x-(4)/(5)y+z=(19)/(5)]:}

Solve for x,y x, y , and z z \newlinex+6y−z=−5−2x−5y+2z=3x−45y+z=195 \begin{array}{l} x+6 y-z=-5 \\ -2 x-5 y+2 z=3 \\ x-\frac{4}{5} y+z=\frac{19}{5} \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Geometryright chevron icon
Sine and cosine of complementary anglesright chevron icon

Full solution

Q. Solve for x,y x, y , and z z \newlinex+6y−z=−5−2x−5y+2z=3x−45y+z=195 \begin{array}{l} x+6 y-z=-5 \\ -2 x-5 y+2 z=3 \\ x-\frac{4}{5} y+z=\frac{19}{5} \end{array}
  1. Write Equations: Write down the system of equations.\newlineWe have the following system of linear equations:\newline11) x+6y−z=−5x + 6y - z = -5\newline22) −2x−5y+2z=3-2x - 5y + 2z = 3\newline33) x−(45)y+z=(195)x - \left(\frac{4}{5}\right)y + z = \left(\frac{19}{5}\right)
  2. Eliminate Fraction: Multiply the third equation by 55 to eliminate the fraction.\newline5(x−(45)y+z)=5×(195)5(x - (\frac{4}{5})y + z) = 5 \times (\frac{19}{5})\newlineThis simplifies to:\newline5x−4y+5z=195x - 4y + 5z = 19\newlineNow we have the system:\newline11) x+6y−z=−5x + 6y - z = -5\newline22) −2x−5y+2z=3-2x - 5y + 2z = 3\newline33) 5x−4y+5z=195x - 4y + 5z = 19
  3. Eliminate Variable xx: Use the method of elimination to eliminate one variable. Let's eliminate xx by adding equation 11 and equation 22.(x+6y−z)+(−2x−5y+2z)=−5+3(x + 6y - z) + (-2x - 5y + 2z) = -5 + 3This simplifies to:−x+y+z=−2-x + y + z = -2Now we have the system:1) −x+y+z=−21)\, -x + y + z = -22) −2x−5y+2z=32)\, -2x - 5y + 2z = 33) 5x−4y+5z=193)\, 5x - 4y + 5z = 19
  4. Eliminate Variable xx: Multiply equation 11 by 22 and add it to equation 22 to eliminate xx.2(−x+y+z)+(−2x−5y+2z)=2(−2)+32(-x + y + z) + (-2x - 5y + 2z) = 2(-2) + 3This simplifies to:−2x+2y+2z−2x−5y+2z=−4+3-2x + 2y + 2z - 2x - 5y + 2z = -4 + 3Combining like terms, we get:−4x−3y+4z=−1-4x - 3y + 4z = -1Now we have the system:11) −x+y+z=−2-x + y + z = -222) −4x−3y+4z=−1-4x - 3y + 4z = -133) 5x−4y+5z=195x - 4y + 5z = 19
  5. Eliminate Variable x: Multiply equation 11 by 55 and add it to equation 33 to eliminate x.\newline5(−x+y+z)+(5x−4y+5z)=5(−2)+195(-x + y + z) + (5x - 4y + 5z) = 5(-2) + 19\newlineThis simplifies to:\newline−5x+5y+5z+5x−4y+5z=−10+19-5x + 5y + 5z + 5x - 4y + 5z = -10 + 19\newlineCombining like terms, we get:\newliney+10z=9y + 10z = 9\newlineNow we have the system:\newline11) −x+y+z=−2-x + y + z = -2\newline22) −4x−3y+4z=−1-4x - 3y + 4z = -1\newline33) y+10z=9y + 10z = 9
  6. Solve for yy: Solve equation 33 for yy.y=9−10zy = 9 - 10zNow we can substitute this expression for yy into equations 11 and 22.
  7. Substitute y into Eq 11: Substitute y=9−10zy = 9 - 10z into equation 11.−x+(9−10z)+z=−2-x + (9 - 10z) + z = -2 This simplifies to:−x+9−9z=−2-x + 9 - 9z = -2 Now solve for x:−x=−2−9+9z-x = -2 - 9 + 9z x=11−9zx = 11 - 9z
  8. Substitute yy into Eq 22: Substitute y=9−10zy = 9 - 10z into equation 22.\newline−4x−3(9−10z)+4z=−1-4x - 3(9 - 10z) + 4z = -1\newlineThis simplifies to:\newline−4x−27+30z+4z=−1-4x - 27 + 30z + 4z = -1\newlineNow solve for xx:\newline−4x=−1+27−34z-4x = -1 + 27 - 34z\newlinex=(28−34z)/−4x = (28 - 34z) / -4\newlinex=−7+(34/4)zx = -7 + (34/4)z\newlinex=−7+(17/2)zx = -7 + (17/2)z
  9. Solve for z: Equate the two expressions for xx and solve for zz.11−9z=−7+(172)z11 - 9z = -7 + (\frac{17}{2})zMultiply through by 22 to eliminate the fraction:22−18z=−14+17z22 - 18z = -14 + 17zCombine like terms:22+14=17z+18z22 + 14 = 17z + 18z36=35z36 = 35zDivide by 3535:z=3635z = \frac{36}{35}z=1.02857142857z = 1.02857142857 (approximately)
  10. Substitute zz into yy: Substitute zz back into the expression for yy.
    y=9−10zy = 9 - 10z
    y=9−10(3635)y = 9 - 10(\frac{36}{35})
    y=9−36035y = 9 - \frac{360}{35}
    y=9−10.2857142857y = 9 - 10.2857142857
    y=−1.2857142857y = -1.2857142857 (approximately)
  11. Substitute zz into xx: Substitute zz back into the expression for xx.
    x=11−9zx = 11 - 9z
    x=11−9(3635)x = 11 - 9(\frac{36}{35})
    x=11−32435x = 11 - \frac{324}{35}
    x=11−9.25714285714x = 11 - 9.25714285714
    x=1.74285714286x = 1.74285714286 (approximately)

More problems from Sine and cosine of complementary angles

Question
Which is equal to sin⁡75∘\sin 75^\circ? \newlineChoices: \newline(A) cos⁡25∘\cos 25^\circ\newline(B) cos⁡15∘\cos 15^\circ\newline(C) sin⁡25∘\sin 25^\circ\newline(D) sin⁡15∘\sin 15^\circ
Get tutor helpright-arrow

Posted 6 months ago

Question
Factor 28+56t+28w 28+56 t+28 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 2(56+112t+56w) 2(56+112 t+56 w) \newlineB 28(1+2t+w) 28(1+2 t+w) \newlinec 4(7+13t+7w) 4(7+13 t+7 w) \newlineD 7(4+8t+4w) 7(4+8 t+4 w)
Get tutor helpright-arrow

Posted 8 months ago

Question
In an election between two candidates Joseph and Judith, 60%60\% of the total number of voters did not vote for Joseph and 50%50\% of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator]\newline(A) 55\newline(B) 1010\newline(C) 2020\newline(D) 3030
Get tutor helpright-arrow

Posted 9 months ago

Question
Jack, Tom, Beth, and Ruth each have a number of marbles. Jack has 1010 marbles, the least, while Tom has 2727 marbles, the highest. Which of the following could be the average of the number of marbles present with all of them, given that no two of them has the same number of marbles?\newlineA) $13A)\ \$13\newlineB) $17B)\ \$17\newlineC) $23C)\ \$23\newlineD) $26D)\ \$26
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline1−6y+5+6x−5x+4 1-6 y+5+6 x-5 x+4
Get tutor helpright-arrow

Posted 8 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline−1−4y3−2x3+5x+2−7−x3 -1-4 y^{3}-2 x^{3}+5 x+2-7-x^{3}
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system:\newlinex+6y=17−x+3y=−8 \begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}
Get tutor helpright-arrow

Posted 8 months ago

Question
For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline7,−35,175,… 7,-35,175, \ldots \newline−5 -5 \newline−42 -42 \newline−15 -\frac{1}{5} \newline4242
Get tutor helpright-arrow

Posted 9 months ago

Question
For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline4x−1,3x−1,2x−1,..  4 x-1, \quad 3 x-1, \quad 2 x-1, \quad \text {.. } \newline11\newline−x -x \newlinex x \newline−1 -1
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system.\newline{x+3y−z=−6 −2x−y+z=10 x−y+3z=2\begin{cases} x+3y-z&=-6 \ -2x-y+z&=10 \ x-y+3z&=2 \end{cases}
Get tutor helpright-arrow

Posted 8 months ago

View all (17)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant