The solution of the system of equations that is given is (2,-1).
Given a system of equations are 5x+y=9 and 3x+2y=4.
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.
The given equations are
5x+y=9 ......(1)
3x+2y=4 ......(2)
Here, the substitution method is used to solve the system of equations.
Find the value of y from equation (1) by subtracting 5x from both sides.
5x+y-5x=9-5x
y=9-5x
To find the value of x substitute the value of y in equation (2).
3x+2(9-5x)=4
Apply the distributive property a(b+c)=ab+ac as
3x+2×9-2×5x=4
3x+18-10x=4
Combine the like terms on the left side as
-7x+18=4
Subtract 18 from both sides and get
-7x+18-18=4-18
-7x=-14
Divide both sides by -7 and get
(-7x)÷(-7)=(-14)÷(-7)
x=2
Substitute the value of x in equation (1) and get
5(2)+y=9
10+y=9
Subtract 10 from both sides
10+y-10=9-10
y=-1
Hence, the solution of system of equations 5x+y=9 and 3x+2y=4 is (2,-1).
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If x=6 and y=3 is 9_______________________________________
The solution to given system of equations is (x, y) = (2, -1)
<em><u>Solution:</u></em>
Given system of equations are:
-1x + 2y = -4 -------- eqn 1
4x + 3y = 5 ------- eqn 2
We can solve the above system of equations by elimination method
<em><u>Multiply eqn 1 by 4</u></em>
4(-1x + 2y = -4)
-4x + 8y = -16 ------ eqn 3
<em><u>Add eqn 2 and eqn 3</u></em>
4x + 3y = 5
-4x + 8y = -16
( + ) --------------------
0x + 11y = -16 + 5
11y = -11
y = -1
<em><u>Substitute y = -1 in eqn 1</u></em>
-1x + 2(-1) = -4
-x -2 = -4
-x = -4 + 2
-x = -2
x = 2
<em><u>Check the answer:</u></em>
Substitute x = 2 and y = -1 in eqn 2
4x + 3y = 5
4(2) + 3(-1) = 5
8 - 3 = 5
5 = 5
Thus the obtained answer is correct
Thus the solution to given system of equations is (x, y) = (2, -1)
Answer:
As the lines are neither parallel nor perpendicular.
Therefore, the correct answer is ''neither''.
Hence, option C is correct.
Step-by-step explanation:
Given
m₁ = 3/2
m₂ = -3/2
We know that when two lines are parallel, they have equal slopes
But
m₁ ≠ m₂
3/2 ≠ -3/2
As the m₁ and m₂ are not equal.
Hence, the lines are not parallel.
We know that when two lines are perpendicular, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = 3/2 × -3/2
= -9/4
= -2.25
As
m₁ × m₂ ≠ -1
Thus, the lines are not perpendicular.
Conclusion:
As the lines are neither parallel nor perpendicular.
Therefore, the correct answer is ''neither''.
Hence, option C is correct.
Answer:
-12
Step-by-step explanation:
(-2)(-3)^2-2(2-5). Original
-2(9)-2(2-5) Distribute Exponents
-18-4+10 Distribute Parentheses
-22+10 Do subtraction
-12 Do Addition