Question

solve the systems of equations
-x+6y= 13
4x-10y= -10
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Answer 1

Let's solve this system of equations using the substitution or elimination method. For this example, we'll use the elimination method because it seems more straightforward with given coefficients.

We have the following system:

1) -x + 6y = 13
2) 4x - 10y = -10

First, we want to manipulate these equations so that adding or subtracting them will eliminate one variable. We can do this by making the coefficients of x or y in both equations to be the same or exact opposites. Multiplying the first equation by 4 will allow us to eliminate the x variable when we add the two equations:

4 * (-x + 6y) = 4 * 13
-4x + 24y = 52

Now we have:

3) -4x + 24y = 52
2) 4x - 10y = -10

Now, if we add equations 3 and 2:

(-4x + 4x) + (24y - 10y) = 52 - 10
0x + 14y = 42

Simplifying, we get:

14y = 42
y = 42 / 14
y = 3

Now we can substitute y = 3 into either of the original equations to find the value of x. Let's use the first equation:

-x + 6(3) = 13
-x + 18 = 13

Now subtract 18 from both sides:

-x = 13 - 18
-x = -5

Divide by -1 to solve for x:

x = 5

Now we have the solutions for both variables:

x = 5
y = 3

So the solution to the system of equations is (5, 3).