solve -15x - 2y = -31, 4x + 6y = 11 using Linear Combination Method?
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To solve the system of equations using the Linear Combination Method, follow these steps:
Step 1: Choose one of the equations and multiply it by a constant so that the coefficients of either x or y are the same in both equations. This will allow you to eliminate one of the variables when you add the two equations together.
Let's choose the first equation, -15x - 2y = -31, and multiply it by 2 to make the coefficient of y the same as the coefficient of y in the second equation. This gives us:
-30x - 4y = -62
Step 2: Now, add the modified equation from Step 1 to the second equation, which will eliminate the variable y.
(-30x - 4y) + (4x + 6y) = -62 + 11
Simplifying the equation, you get:
-26x + 2y = -51
Step 3: Now you have a new equation with only one variable. Solve the equation for x or y.
Let's solve this equation for x:
-26x = -51 - 2y
Divide both sides by -26:
x = (51 + 2y)/26
Step 4: Substitute the value of x into one of the original equations to find the value of the remaining variable. Let's use the first equation, -15x - 2y = -31.
-15((51 + 2y)/26) - 2y = -31
Step 5: Simplify and solve for y.
-15(51 + 2y) - 52y = -31 * 26
-765 - 30y - 52y = -806
-82y = -806 - 765
-82y = -1571
y = (-1571)/(-82)
y ≈ 19.14
Step 6: Substitute the value of y into the equation solved in Step 3 to find the value of x.
x = (51 + 2(19.14))/26
x ≈ 2.07
So, the solution to the system of equations is approximately x ≈ 2.07, y ≈ 19.14.