Solve −3x − 4y = −31, 4x + 4y = 36
Worked out line by line the way a teacher would write it.
Answer
| Solution | x = 5, y = 4 |
Step-by-step solution
6 steps-
1 The system, with the equations numbered\begin{aligned}- 3 x - 4 y &= -31 & (1)\\ 4 x + 4 y &= 36 & (2)\end{aligned}
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2 Add the two equations to eliminate y
Adding or subtracting two true equations gives another true equation. Because the y-terms match, they cancel, leaving one equation in one unknown.
x = 5 -
3 Substitute x = 5 into equation (1)
Once one unknown is known, putting its value into an earlier equation gives the other one.
- 4 y - 3 \cdot 5 = -31 -
4 Add 15 to both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
- 4 y = -16Move the constant terms to the right.
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5 Divide both sides by -4
Dividing both sides by -4 undoes the multiplication by -4, so the variable is left on its own. Both sides change in the same way, so the equation stays true (dividing by 0 is the one thing that is never allowed).
y = \frac{-16}{-4} -
6 Simplifyy = 4
Check by substitution
| Equation | Left side | Right side | |
|---|---|---|---|
| (1) | −31 | −31 | ✓ |
| (2) | 36 | 36 | ✓ |
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