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Answer: x = -1 and y = 3
Step-by-step explanation:
[tex]10x - 5y = -25 \\10x + 8y = 14[/tex]
Let's start by solving [tex]10x - 5y = -25[/tex] for [tex]x[/tex]
[tex]10x - 5y=-25[/tex]
Add 5y to both sides
[tex]10x - 5y + 5y = -25+5y \\10x = 5y - 25[/tex]
Now we need to divide both sides by 10
[tex]\frac{10x}{10} = \frac{5y-25}{10}[/tex]
[tex]x = \frac{1}{2} y + \frac{-5}{2}[/tex]
That's not the answer for x. We are not done yet :)
Now we need to substitute [tex]\frac{1}{2} y + \frac{-5}{2}[/tex] for [tex]x[/tex]
[tex]10x + 8y = 14\\10(\frac{1}{2} y + \frac{-5}{2} + 8y = 14[/tex]
Now we need to simply both sides
[tex]13y - 25 = 14[/tex]
Now we need to add 25 to both sides
[tex]13y - 25 + 25 = 14 + 25 \\13y = 39 \\y = \frac{39}{13} \\y=3[/tex]
We have the valuee for y! Now we need to find the value for x
To find the value of x, we need to substitute 3 for y in:
[tex]x = \frac{1}{2} y + \frac{-5}{2} \\x = \frac{1}{2} 3 + \frac{-5}{} \\x = -1[/tex]
Therefore,
The answer is x = -1 and y = 3
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