Use substitution to solve 3x + 3y = 6 andy = x + 1.
Solve the linear system of equations using substitution.
x – 7y = 23
4x – 3y = 42
Solve the system using the substitution method.
3x + 4y = 11
x – 7y = 12
Use substitution to solve a + 2b = 1 and 2a – 3b = 23.
Use elimination to solve p + 3q = 16 andp + q = 6. State whether the equations are consistent or inconsistent and dependent or independent.
Use elimination to solve 3m – 3n = 13 and – 4m + 4n = –8. State whether the equations are consistent or inconsistent and dependent or independent.
Find the value of x and y by using either substitution or elimination.
y = 4x – 17
2.3a – 0.8b = –8.5
0.6a + 0.7b = –0.4
Solve the given system by using the Linear–Combination Method (also known as the Elimination Method).
Solve the system using the linear combination method.
–4x + 6y = 3
5x – 12y = –6
Solve the system of equations using linear combinations.
5x + 30y = 15
4x + 15y = 9
Graph the following system and solve.
3x + 2y = 2
–2x – 4y = 4
Determine the number of solutions for the system:
4x + y = 8
3x + 2y = 1
Solve: 0.05m + 0.03n = –5 and 0.02m + 0.05n = 17.
Solve:
Solve: x + 3y = 1 and 5x = 3(3y + 4) + 1
Solve the system of equations:
3x +y = 1 and 3x + 4y = 22
x + 5y = 7 and 4x – 3y = 5
Solve the system using any algebraic method.
2x – 6y = 12
–3x + 5y = –18
x + y = 3x –2 and x – y = 2 – x
4y =x – 3y – 2 and 4x = 3x – y – 2
Write the system of equations in the slope–intercept form. By comparing the slopes and y–intercepts determine whether the system of equations are consistent.
4x – 5y = 20 and 5x – 4y= 20
Solve the system of equations.
Find the coordinate of the vertices.
2x + 3y = 12
x + y = 6
4x + 3y = 18
What conditions must be placed on the constants such that the system of equations has a unique solution.
Sketch the given system.
y = 2x2
y = 2x
And check whether the system is consistent or inconsistent. If consistent, solve the equations using substitution.
From the given choices, complete the sentence.
When the graph of a system is two different parallel lines, the system has a solution.
(a) always
(b) sometimes
(c) never
Use substitution to solve 3x + 3y = 6 and y = x + 1.
Use elimination to solve p + 3q = 16 and p + q = 6. State whether the equations are consistent or inconsistent and dependent or independent.
3x + y = 1 and 3x + 4y = 22
4y = x – 3y – 2 and 4x = 3x – y – 2
has a solution.
