Question

Solve using the addition method. What is the x-value of the solution to the system?

2x – 3y = -1
3x + 4y = 24

4

3

2

none of the above

Answer 1

2x-3y=-1_3x+4y=24

Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 12.
4*(2x-3y=-1)_3*(3x+4y=24)

Multiply each equation by the value that makes the coefficients of y equal. This value is found by dividing the least common multiple of the coefficients of y by the current coefficient. In this case, the least common multiple is 12.
4*(2x-3y)=4(-1)_3*(3x+4y)=3(24)

Multiply 4 by each term inside the parentheses.
4*(2x-3y)=-4_3*(3x+4y)=3(24)

Multiply 4 by each term inside the parentheses.
8x-12y=-4_3*(3x+4y)=3(24)

Multiply 3 by each term inside the parentheses.
8x-12y=-4_3*(3x+4y)=72

Multiply 3 by each term inside the parentheses.
8x-12y=-4_9x+12y=72

Add the two equations together to eliminate y from the system.
9x+12y=72_<U>8x-12y=-4<u>_17x =68

Divide each term in the equation by 17.
x=4

Substitute the value found for x into the original equation to solve for y.
8(4)-12y=-4

Multiply 8 by each term inside the parentheses.
32-12y=-4

Move all terms not containing y to the right-hand side of the equation.
-12y=-36

Divide each term in the equation by -12.
y=3

This is the final solution to the independent system of equations.
x=4_y=3