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Sagot :
To solve the system of equations using the elimination method, we perform the following steps:
Given:
[tex]\[ \begin{array}{l} 2x + 3y = 18 \quad \text{(1)} \\ 3x - 3y = 12 \quad \text{(2)} \end{array} \][/tex]
Step 1: Eliminate [tex]\( y \)[/tex]
To eliminate [tex]\( y \)[/tex], we can add the two equations directly. Observe that in equation (2), the coefficient of [tex]\( y \)[/tex] is [tex]\(-3\)[/tex], which is the negative of the coefficient of [tex]\( y \)[/tex] in equation (1). Adding them will cancel out [tex]\( y \)[/tex].
So, add (1) and (2):
[tex]\[ (2x + 3y) + (3x - 3y) = 18 + 12 \][/tex]
Simplifying:
[tex]\[ 2x + 3x + 3y - 3y = 30 \][/tex]
[tex]\[ 5x = 30 \][/tex]
Dividing both sides by 5:
[tex]\[ x = 6 \][/tex]
Step 2: Substitute [tex]\( x = 6 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]
We can use either equation (1) or (2). Let's use equation (1):
[tex]\[ 2x + 3y = 18 \][/tex]
Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[ 2(6) + 3y = 18 \][/tex]
[tex]\[ 12 + 3y = 18 \][/tex]
Subtract 12 from both sides:
[tex]\[ 3y = 6 \][/tex]
Divide both sides by 3:
[tex]\[ y = 2 \][/tex]
Step 3: Write down the solution
The solution to the system of equations is [tex]\( (x, y) = (6, 2) \)[/tex].
So, the answer is:
[tex]\[ B. (6, 2) \][/tex]
Given:
[tex]\[ \begin{array}{l} 2x + 3y = 18 \quad \text{(1)} \\ 3x - 3y = 12 \quad \text{(2)} \end{array} \][/tex]
Step 1: Eliminate [tex]\( y \)[/tex]
To eliminate [tex]\( y \)[/tex], we can add the two equations directly. Observe that in equation (2), the coefficient of [tex]\( y \)[/tex] is [tex]\(-3\)[/tex], which is the negative of the coefficient of [tex]\( y \)[/tex] in equation (1). Adding them will cancel out [tex]\( y \)[/tex].
So, add (1) and (2):
[tex]\[ (2x + 3y) + (3x - 3y) = 18 + 12 \][/tex]
Simplifying:
[tex]\[ 2x + 3x + 3y - 3y = 30 \][/tex]
[tex]\[ 5x = 30 \][/tex]
Dividing both sides by 5:
[tex]\[ x = 6 \][/tex]
Step 2: Substitute [tex]\( x = 6 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]
We can use either equation (1) or (2). Let's use equation (1):
[tex]\[ 2x + 3y = 18 \][/tex]
Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[ 2(6) + 3y = 18 \][/tex]
[tex]\[ 12 + 3y = 18 \][/tex]
Subtract 12 from both sides:
[tex]\[ 3y = 6 \][/tex]
Divide both sides by 3:
[tex]\[ y = 2 \][/tex]
Step 3: Write down the solution
The solution to the system of equations is [tex]\( (x, y) = (6, 2) \)[/tex].
So, the answer is:
[tex]\[ B. (6, 2) \][/tex]
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