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4x + 5y = 11
y-3x = -13

1 Answer

4 votes

Answer:

x=4 y=-1

Explanation:

To solve this system of linear equations, you can use the method of substitution or elimination. I'll use the elimination method here:

Let's first multiply the second equation by 4 to make it easier to eliminate one of the variables:

4x + 5y = 11

4(y - 3x) = 4(-13)

Now, distribute the 4 on the left side of the second equation:

4x + 5y = 11

4y - 12x = -52

Now, you can add the two equations together to eliminate the variable x:

(4x + 5y) + (4y - 12x) = 11 - 52

Combine like terms on both sides:

4x - 12x + 5y + 4y = -41

-8x + 9y = -41

Now, you have a single equation with one variable:

-8x + 9y = -41

Now, solve for one variable. Let's solve for y:

9y = -41 + 8x

9y = 8x - 41

y = (8x - 41)/9

Now that you have the expression for y, you can substitute it into one of the original equations to solve for x. I'll use the first equation:

4x + 5((8x - 41)/9) = 11

Now, you can solve for x:

4x + (40x - 205)/9 = 11

To eliminate the fraction, multiply both sides by 9:

9(4x) + 40x - 205 = 99

36x + 40x - 205 = 99

Combine like terms:

76x - 205 = 99

Now, isolate x:

76x = 99 + 205

76x = 304

Now, divide by 76:

x = 304/76

x = 4

Now that you have found the value of x, you can substitute it back into either equation to solve for y. I'll use the second equation:

y - 3(4) = -13

y - 12 = -13

Add 12 to both sides:

y = -13 + 12

y = -1

So, the solution to the system of equations is x = 4 and y = -1.

User Quintin
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