Math 1508 NameD. WilsonChapter 7, Part I: Systems of Equations1. The Substitution Method for Two Equations• Choose an equation. Then solve for one of the variables.• Substitute this new expression into the other equation. You should now have an equation interms of one variable only. Solve the equation.• Find the value of the other variable.• Check your solution by plugging into both original equations.2. The Elimination Method for Two Equations• Obtain coefficients for x (or y) that differ only in sign by multiplying all terms of one or bothequations by suitably chosen constants,• Add the equations to eliminate one variable, and solve the resulting equation.• Find the value of the other variable.• Check your solution by plugging into both original equations.3. Solve this system by substitution.(2x + y = 0x3− 5x =y24. Solve this system by using substitution or elimination.2.1x + 2.2y = 4.46.2x − 3.3y = 6.65. Back-Substitution• You should be able to solve for one variable right away. Usually, the system is triangular.• After solving for one variable, substitute to solve for another variable.• Substitute into the next equation to solve for yet another variable. Repeat this process asneeded.• Check your solution by plugging into all original equations.6. Solve this system by back-substitution.4x − 3y − 2z = −26y − 5z = −11z = 77. Gaussian Elimination This is a process of solving a system of equations by first making thesystem triangular. These are the row operations allowed to turn any system into an equivalent, buttriangular, system:• Interchange two equations.• Multiply one of the equations by a nonzero constant.• Add a multiple of one of the equations to another equation to replace the latter equation.8. Use Gaussian Elimination to solve the systems.(a)x − 2y + 3z = 3−x + 3y − 5z = 52x + 0y − 3z = 4(b)x + y + z = 4x − 5y + 3z = 63y + 5z = 17(c)x + 2y − 7z = −42x + y + z = 133x + 9y − 36z = −33(d)3x + 2y − z = 92x − y + 2z = −44x − 2y + 7z =