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Solve the system of equations.

[tex]\[ 10x - 9y = 24 \][/tex]

[tex]\[ y = x - 2 \][/tex]

[tex]\[ x = \square \][/tex]

[tex]\[ y = \square \][/tex]

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Sagot :

GinnyAnsweridn
To solve the given system of equations:

[tex]\[ 10x - 9y = 24 \][/tex]
[tex]\[ y = x - 2 \][/tex]

we will use the second equation to substitute [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] into the first equation. Let's proceed step by step:

1. Start with the second equation:
[tex]\[ y = x - 2 \][/tex]

2. Substitute [tex]\( y \)[/tex] in the first equation:
[tex]\[ 10x - 9(x - 2) = 24 \][/tex]

3. Distribute the -9 through the parentheses:
[tex]\[ 10x - 9x + 18 = 24 \][/tex]

4. Simplify the equation:
[tex]\[ x + 18 = 24 \][/tex]

5. Solve for [tex]\( x \)[/tex] by subtracting 18 from both sides:
[tex]\[ x = 24 - 18 \][/tex]
[tex]\[ x = 6 \][/tex]

Now that we have [tex]\( x \)[/tex], we can substitute it back into the second equation to find [tex]\( y \)[/tex]:

6. Substitute [tex]\( x = 6 \)[/tex] into [tex]\( y = x - 2 \)[/tex]:
[tex]\[ y = 6 - 2 \][/tex]
[tex]\[ y = 4 \][/tex]

Therefore, the solutions to the system of equations are:
[tex]\[ x = 6 \][/tex]
[tex]\[ y = 4 \][/tex]
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