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Sagot :
Sure, let's solve the system of linear equations step-by-step:
[tex]\( \left\{ \begin{array}{l} y = 7 - 2x \quad \quad \quad \quad(1)\\ 4x + y = 5 \quad \quad \quad(2) \end{array} \right. \)[/tex]
Step 1: Substitute [tex]\( y \)[/tex] from equation (1) into equation (2).
From equation (1), we know:
[tex]\( y = 7 - 2x \)[/tex]
Now, substitute this expression for [tex]\( y \)[/tex] into equation (2):
[tex]\( 4x + (7 - 2x) = 5 \)[/tex]
Step 2: Simplify and solve for [tex]\( x \)[/tex].
Combine like terms in the equation:
[tex]\( 4x + 7 - 2x = 5 \)[/tex]
Simplify it further:
[tex]\( 2x + 7 = 5 \)[/tex]
Subtract 7 from both sides:
[tex]\( 2x = 5 - 7 \)[/tex]
[tex]\( 2x = -2 \)[/tex]
Divide both sides by 2:
[tex]\( x = -1 \)[/tex]
Step 3: Substitute [tex]\( x = -1 \)[/tex] back into equation (1) to solve for [tex]\( y \)[/tex].
Now that we have the value of [tex]\( x \)[/tex], substitute it back into equation (1):
[tex]\( y = 7 - 2(-1) \)[/tex]
Simplify:
[tex]\( y = 7 + 2 \)[/tex]
[tex]\( y = 9 \)[/tex]
Conclusion:
The solution to the system of linear equations is:
[tex]\[ x = -1, \quad y = 9 \][/tex]
So, the solution in ordered pair form is [tex]\((-1, 9)\)[/tex].
[tex]\( \left\{ \begin{array}{l} y = 7 - 2x \quad \quad \quad \quad(1)\\ 4x + y = 5 \quad \quad \quad(2) \end{array} \right. \)[/tex]
Step 1: Substitute [tex]\( y \)[/tex] from equation (1) into equation (2).
From equation (1), we know:
[tex]\( y = 7 - 2x \)[/tex]
Now, substitute this expression for [tex]\( y \)[/tex] into equation (2):
[tex]\( 4x + (7 - 2x) = 5 \)[/tex]
Step 2: Simplify and solve for [tex]\( x \)[/tex].
Combine like terms in the equation:
[tex]\( 4x + 7 - 2x = 5 \)[/tex]
Simplify it further:
[tex]\( 2x + 7 = 5 \)[/tex]
Subtract 7 from both sides:
[tex]\( 2x = 5 - 7 \)[/tex]
[tex]\( 2x = -2 \)[/tex]
Divide both sides by 2:
[tex]\( x = -1 \)[/tex]
Step 3: Substitute [tex]\( x = -1 \)[/tex] back into equation (1) to solve for [tex]\( y \)[/tex].
Now that we have the value of [tex]\( x \)[/tex], substitute it back into equation (1):
[tex]\( y = 7 - 2(-1) \)[/tex]
Simplify:
[tex]\( y = 7 + 2 \)[/tex]
[tex]\( y = 9 \)[/tex]
Conclusion:
The solution to the system of linear equations is:
[tex]\[ x = -1, \quad y = 9 \][/tex]
So, the solution in ordered pair form is [tex]\((-1, 9)\)[/tex].
Answer:
x = -1
y= 9
Explanation:
Use substitution to solve this question!
First, substitute y in the second equation:
4x + (7-2x) = 5
Now solve for x
4x + 7 - 2x = 5
2x +7= 5
2x = -2
x = -1
Now you have X! To find y, plug x into the first equation and solve for y:
y = 7- 2(-1)
y = 7+2
y= 9
The solution to the system of equations is
x = -1
y= 9
Check you answer by plugging x and y to the second equation to see if it equals 5!
Learn more about systems of equations here: https://brainly.com/question/7808225
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