1.
Solve the linear system.
4$x$ + 5$y$ = 45
7$x$ - 5$y$ = 10
Solution:
4x + 5y = 45
[Equation 1.]
7x - 5y = 10
____________
[Equation 2.]
11x = 55
[Add the equations.]
x = 5
[Solve for x.]
4(5) + 5y = 45
[Substitute x = 5 in equation 1.]
20 + 5y = 45
[Multiply.]
5y = 25
[Subtract 20 from each side.]
y = 5
[Solve for y.]
The solution for the linear system is (5, 5).
Correct answer : (3)
2.
Solve the linear system.
-$x$ + $y$ = -20
17$x$ - $y$ = 68
Solution:
-x + y = -20
[Equation 1.]
17x - y = 68
___________
[Equation 2.]
16x = 48
[Add the equations.]
x = 3
[Solve for x.]
-3 + y = -20
[Substitute x = 3 in Equation 1.]
y = -17
[Solve for y.]
So, the solution for the linear system is (3, -17).
Correct answer : (2)
3.
Which of the following ordered pairs satisfies the linear system?
3$x$ - 4$y$ = 4
5$x$ + 4$y$ = 28
Solution:
3x - 4y = 4
[Equation 1.]
5x + 4y = 28
______________
[Equation 2.]
8x = 32
[Add the equations.]
x = 4
[Solve for x.]
3(4) - 4y = 4
[Substitute 4 for x in equation 1.]
y = 2
[Solve for y.]
The solution for the linear system is (4, 2).
Correct answer : (2)
4.
Solve the linear system.
-5$x$ - $y$ = -15
-3$x$ + $y$ = -1
Solution:
-5x - y = -15
[Equation 1.]
-3x + y = -1
______________
[Equation 2.]
-8x = -16
[Add the equations.]
x = 2
[Solve for x.]
-5(2) - y = -15
[Substitute x = 2 in Equation 1.]
y = 5
[Solve for y.]
The solution for the linear system is (2, 5).
Correct answer : (2)
5.
Solve the linear system.
$x$ - 3$y$ = -13
-$x$ + 7$y$ = 37
Solution:
x - 3y = -13
[Equation 1.]
-x + 7y = 37
____________
[Equation 2.]
4y = 24
[Add the equations.]
y = 6
[Solve for y.]
x - 3(6) = -13
[Substitute y = 6 in Equation 1.]
x = 5
[Solve for x.]
So, the solution for the linear system is (5, 6).
Correct answer : (1)
6.
Solve the linear system.
3$x$ + $y$ = 22
-4$x$ - 2$y$ = -26
Solution:
Eliminate x from both the equations by making the coefficient of x in one equation opposite to the other.
12x + 4y = 88
[Multiply Equation 1 by 4.]
-12x - 6y = -78
_______________
[Multiply Equation 2 by 3.]
-2y = 10
[Add the equations.]
y = -5
[Solve for y.]
3x + (-5) = 22
[Substitute y = -5 in Equation 1.]
x = 9
[Solve for x.]
The solution for the linear system is (9, -5).
Correct answer : (3)
7.
Which of the following ordered pairs satisfies the given linear system?
$x$ - 4$y$ = -22
-3$x$ - 5$y$ = -36
Solution:
3x - 12y = -66
[Multiply Equation 1 by 3.]
-3x - 5y = -36
______________
[Equation 2.]
-17y = -102
[Add the Equations.]
y = 6
[Solve for y.]
x - 4(6) = -22
[Substitute y = 6 in Equation 1.]
x - 24 = -22
[Multiply.]
x = -22 + 24
[Add 24 to each side.]
x = 2
[Solve for x.]
So, the solution for the linear system is (2, 6).
Correct answer : (3)
8.
Which of the following ordered pairs satisfies the given linear system?
-$x$ + $y$ = -2 --- Equation 1
-3$x$ - 3$y$ = -30 --- Equation 2
Solution:
-x - y = -10
[Divide Equation 2 by 3.]
-x + y = -2
[Equation 1.]
-x - y = -10
_____________
[Revised Equation 2.]
-2x = -12
[Add Equation 1 and revised Equation 2.]
x = 6
[Solve for x.]
-6 + y = -2
[Substitute 6 for x in revised Equation 2.]
y = 4
[Add 6 to each side.]
The solution for the linear system is (6, 4).
Correct answer : (2)
9.
Which of the following solutions satisfies the given linear system?
5$x$ - $y$ = -2
-4$x$ + 5$y$ = -11
Solution:
25x - 5y = -10
[Multiply Equation 1 by 5.]
-4x + 5y = -11
______________
[Multiply Equation 2 by 1.]
21x = -21
[Add the equations.]
x = -1
[Solve for x.]
5(-1) - y = -2
[Substitute x = -1 in Equation 1.]
y = -3
[Solve for y.]
Solution for the linear system is (-1, -3).
Correct answer : (3)
10.
Which of the following ordered pairs satisfies the given linear system?
-5$x$ + 4$y$ = -4
4$y$ = 4 + 3$x$
Solution:
-5x + 4y = -4
[Equation 1.]
3x - 4y = -4
____________
[Rearrange Equation 2 and multiply with -1.]
-2x = -8
[Add the equations.]
x = 4
[Solve for x.]
-5(4) + 4y = -4
[Substitute 4 for x in Equation 1.]
-20 + 4y = -4
[Multiply.]
4y = 16
[Add 20 on each side.]
y = 4
[Solve for y.]
Solution for the linear system is (4, 4).
Correct answer : (1)