Solve the following system of equations algebraically, and check: x+2y=4 y=2x+7 Answer: x=?,

Kathleen Rausch

Kathleen Rausch

Answered question

2021-12-29

Solve the following system of equations algebraically, and check:
x+2y=4
y=2x+7
Answer: x=?,y=?

Answer & Explanation

Robert Pina

Robert Pina

Beginner2021-12-30Added 42 answers

Algebraically resolve the system of equations
x+2y=4 (1) 
y=2x+7 (2) 
By substitution method, substitute (2) in (1), we get 
x+2(2x+7)=4 
x+4x+14=4 
5x=414=10 
x=105=2 
From (2), we set y=2(2)+7 
y=4+7=3 
As a result, the answer is:
x=2  and  y=3 
Putting x=2,y=3 in (1) and (2) were 
2+2(3)=1 
4=4, which is true 
and 3=2(2)+7 
3=4+7 
3=3, which is true.

Paul Mitchell

Paul Mitchell

Beginner2021-12-31Added 40 answers

Explanation:
First, define one variable (let's do x) in terms of the other (y). Using the first equation, we can conclude that x=2y+4. Then, we can substitute 2y+4 into anywhere we see x in the second equation, so:
2(2y+4)y=7
4y+8y=7
3y+8=7
3y=1
y=13
Then, plug y back into the first equation to find x.
x2(13)=4
x+23=4
x=103
karton

karton

Expert2022-01-04Added 613 answers

Put the system of linear equations into standard form:
x+2y=4
2x-y=-7
Solution:
x =-2
y = 3
system matrix
[1221]
inverse of system matrix
[0.20.40.40.2]
determinant of system matrix =-5
graph:
y=(12)x+2
y=2x+7

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