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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