Why do we add two equations in elimination and not subtract?
0
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If you had the equation $2x + 5y = 1$ and $2x + 42y = 149$ or whatever (the numbers probably don't work but that's not important), how come we can't subtract the two equations to isolate for $y$ in this case? Why do we add equations?
algebra-precalculus
edited Jan 14 at 16:23
user26857
39.4k124183
asked Jan 14 at 1:51
mingming
3956
$endgroup$
add a comment |
0
$begingroup$
If you had the equation $2x + 5y = 1$ and $2x + 42y = 149$ or whatever (the numbers probably don't work but that's not important), how come we can't subtract the two equations to isolate for $y$ in this case? Why do we add equations?
algebra-precalculus
edited Jan 14 at 16:23
user26857
39.4k124183
asked Jan 14 at 1:51
mingming
3956
$endgroup$
8
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
3
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
2
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04
add a comment |
0
0
0
$begingroup$
If you had the equation $2x + 5y = 1$ and $2x + 42y = 149$ or whatever (the numbers probably don't work but that's not important), how come we can't subtract the two equations to isolate for $y$ in this case? Why do we add equations?
algebra-precalculus
edited Jan 14 at 16:23
user26857
39.4k124183
asked Jan 14 at 1:51
mingming
3956
$endgroup$
If you had the equation $2x + 5y = 1$ and $2x + 42y = 149$ or whatever (the numbers probably don't work but that's not important), how come we can't subtract the two equations to isolate for $y$ in this case? Why do we add equations?
algebra-precalculus
algebra-precalculus
edited Jan 14 at 16:23
user26857
39.4k124183
asked Jan 14 at 1:51
mingming
3956
edited Jan 14 at 16:23
user26857
39.4k124183
asked Jan 14 at 1:51
mingming
3956
edited Jan 14 at 16:23
user26857
39.4k124183
edited Jan 14 at 16:23
user26857
39.4k124183
edited Jan 14 at 16:23
user26857
39.4k124183
39.4k124183
asked Jan 14 at 1:51
mingming
3956
asked Jan 14 at 1:51
mingming
3956
asked Jan 14 at 1:51
mingming
3956
3956
8
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
3
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
2
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04
add a comment |
8
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
3
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
2
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04
8
8
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
3
3
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
2
2
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04
add a comment |
0
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8
$begingroup$
Who said you can't subtract?
$endgroup$
– Randall
Jan 14 at 1:52
3
$begingroup$
Whether to first multiply or divide, and then add or subtract, depends on the particular coefficients and which variable you are trying to eliminate. In your example, subtracting makes the most sense as it will isolate $y$, allowing you to solve for it and then substitute back to solve for $x$. Is the issue that the examples you have seen always did addition, so you thought you weren't allowed to subtract? Also, note that multiplying by $-1$ and then adding is the same as subtracting so, in theory, you could always just add.
$endgroup$
– John Omielan
Jan 14 at 1:55
2
$begingroup$
Since you could first multiply an equation through by $-1,$ both adding and subtracting two equations are OK.
$endgroup$
– coffeemath
Jan 14 at 2:01
$begingroup$
Ah I'm dumb, I just watched like 2 videos on elimination that said to add so I assumed that was the rule lol, my bad
$endgroup$
– ming
Jan 14 at 2:04