Solve the following system:
{2 x + 4 y = -32
y - 3 x = 6
In the second equation, look to solve for y:
{2 x + 4 y = -32
y - 3 x = 6
Add 3 x to both sides:
{2 x + 4 y = -32
y = 3 x + 6
Substitute y = 3 x + 6 into the first equation:
{2 x + 4 (3 x + 6) = -32
y = 3 x + 6
2 x + 4 (3 x + 6) = (12 x + 24) + 2 x = 14 x + 24:
{14 x + 24 = -32
y = 3 x + 6
In the first equation, look to solve for x:
{14 x + 24 = -32
y = 3 x + 6
Subtract 24 from both sides:
{14 x = -56
y = 3 x + 6
Divide both sides by 14:
{x = -4
y = 3 x + 6
Substitute x = -4 into the second equation:
Answer: | x = -4 and y = -6
+2441 To solve for x and y, first solve for a variable and plug it into the other equation. Since you specified solving by substitution, I'll use that method. Here are your 2 equations:
1. \(2x+4y=-32\)
2. \(-3x+y=6\)
I'll solve for y in the second equation because it has a coefficient of 1.
| \(-3x+y=6\) | To isolate y, add 3x to both sides. |
| \(y=6+3x\) | |
Now that I have solved for y in one equation, substitute y in the other.
| \(2x+4y=-32\) | In the previous calculation, we deduced that y=6+3x, so replace y. |
| \(2x+4(6+3x)=-32\) | Distribute the 4 into the parentheses to ease the simplification process. |
| \(2x+24+12x=-32\) | Combine the like terms, specifically 2x and 12x. |
| \(14x+24=-32\) | Subtract 24 on both sides. |
| \(14x=-56\) | Divide by 14 on both sides to isolate x. |
| \(x=-4\) | |
Plug x into an equation and solve for y. I'll plug it into equation 2
| \(-3x+y=6\) | Substitute the calculated value for x, -4. |
| \(-3(-4)+y=6\) | Simplify -3*-4. |
| \(12+y=6\) | Subtract 12 on both sides |
| \(y=-6\) | |
Therefore, the solution set is (-4,-6)
x+y=97; x-y=39 / using elimination method/ SHOW WORK
Solve the following system:
{x + y = 97 | (equation 1)
x - y = 39 | (equation 2)
Subtract equation 1 from equation 2:
{x + y = 97 | (equation 1)
0 x - 2 y = -58 | (equation 2)
Divide equation 2 by -2:
{x + y = 97 | (equation 1)
0 x+y = 29 | (equation 2)
Subtract equation 2 from equation 1:
{x+0 y = 68 | (equation 1)
0 x+y = 29 | (equation 2)
Collect results:
Answer: | x = 68 and y = 29
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