QuestionAugust 27, 2025

Solve the system of linear equations using the elimination method. 7x-3y=-9 5x-4y=-25 no solution (10,3) (-3,-4) (3,10)

Solve the system of linear equations using the elimination method. 7x-3y=-9 5x-4y=-25 no solution (10,3) (-3,-4) (3,10)
Solve the system of linear equations using the elimination method.
7x-3y=-9
5x-4y=-25
no solution
(10,3)
(-3,-4)
(3,10)

Solution
4.2(241 votes)

Answer

(3,10) Explanation 1. Align the equations for elimination Multiply the first equation by 5 and the second by 7 to align coefficients of x. - First equation: 5(7x - 3y) = 5(-9) becomes 35x - 15y = -45 - Second equation: 7(5x - 4y) = 7(-25) becomes 35x - 28y = -175 2. Eliminate x Subtract the first modified equation from the second. - (35x - 28y) - (35x - 15y) = -175 + 45 - Simplifies to -13y = -130 3. Solve for y Divide both sides by -13. - y = \frac{-130}{-13} = 10 4. Substitute y back to find x Use the first original equation 7x - 3y = -9. - Substitute y = 10: 7x - 3(10) = -9 - Simplify: 7x - 30 = -9 - Solve for x: 7x = 21, so x = 3

Explanation

1. Align the equations for elimination<br /> Multiply the first equation by 5 and the second by 7 to align coefficients of $x$.<br />- First equation: $5(7x - 3y) = 5(-9)$ becomes $35x - 15y = -45$<br />- Second equation: $7(5x - 4y) = 7(-25)$ becomes $35x - 28y = -175$<br /><br />2. Eliminate $x$<br /> Subtract the first modified equation from the second.<br />- $(35x - 28y) - (35x - 15y) = -175 + 45$<br />- Simplifies to $-13y = -130$<br /><br />3. Solve for $y$<br /> Divide both sides by -13.<br />- $y = \frac{-130}{-13} = 10$<br /><br />4. Substitute $y$ back to find $x$<br /> Use the first original equation $7x - 3y = -9$.<br />- Substitute $y = 10$: $7x - 3(10) = -9$<br />- Simplify: $7x - 30 = -9$<br />- Solve for $x$: $7x = 21$, so $x = 3$
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