Question

Solve this system of linear equations. Separate

the x- and y-values with a comma.
9x - 19y = 74
3x + 3y = 6

Answer 1

Answer is ( 4, -2 )

Step by step

We can solve this standard form equation with elimination.

Given

9x - 19y = 74 ➡️ Equation 1

3x + 3y = 6 ➡️ Equation 2

If we multiply EQ.2 by -3 we can eliminate x

-3 ( 3x + 3y = 6)
-9x -9y = -18

Now we have

9x - 19y = 74
-9x -9y = -18
———————- add like terms
0 - 28y = 56
Divide both sides by -28 to solve y

-28/-28 y = 56/ -28

y = - 2

Now substitute value of y = -2 into either equation to solve for x

3x + 3y = 6
3x + 3(-2) = 6
3x - 6 = 6
Add 6 to both sides to isolate x

3x -6 +6 = 6 +6
Simplify

3x = 12
Divide both sides by 3 to solve x

3/3 x = 12/3
x = 4

Your answer is ( 4, -2)

I graphed it to prove my solution

Answer 2

Explanation:

We can start by solving the second equation for one of the variables. Let's solve for y:

3x + 3y = 6

3y = 6 - 3x

y = 2 - x

Now we can substitute this expression for y into the first equation:

9x - 19y = 74

9x - 19(2 - x) = 74 (substituting y = 2 - x)

9x - 38 + 19x = 74

28x = 112

x = 4

Now we can use this value to find y:

y = 2 - x

y = 2 - 4

y = -2

Therefore, the solution to the system of equations is x = 4 and y = -2.

Hopes this helps