Question
2x+5y=2 3x+4y=-4 Solve by elimination
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Answer to a math question 2x+5y=2 3x+4y=-4 Solve by elimination
Jayne
4.499 Answers
1. Multiply the first equation by 3 and the second equation by 2 to make the coefficients of \( x \) equal:
2x + 5y = 2 \quad \rightarrow \quad 3(2x + 5y) = 3 \cdot 2
\Rightarrow 6x + 15y = 6
3x + 4y = -4 \quad \rightarrow \quad 2(3x + 4y) = 2 \cdot (-4)
\Rightarrow 6x + 8y = -8
2. Subtract the second modified equation from the first:
(6x + 15y) - (6x + 8y) = 6 - (-8)
\Rightarrow 7y = 14
3. Divide by 7 to solve for \( y \):
y = 2
4. Substitute \( y = 2 \) back into the first original equation to solve for \( x \):
2x + 5(2) = 2
\Rightarrow 2x + 10 = 2
\Rightarrow 2x = 2 - 10
\Rightarrow 2x = -8
\Rightarrow x = -4
Final Solution:
x=-4,\,y=2
2. Subtract the second modified equation from the first:
3. Divide by 7 to solve for \( y \):
4. Substitute \( y = 2 \) back into the first original equation to solve for \( x \):
Final Solution:
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