Question

System of equations

2x + 3y = 4
3x + 5y = 7
10x + 15y = 20
-9x - 15y = -21
Find the solution of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
Enter the correct answer.
DONE

Answer 1

Answer:-₍1,3₎

Explanation:

To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:

$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$

$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$

Adding the equations, we get:

$10x + 15y - 9x - 15y = 20 - 21$

Simplifying, we get:

$x = -1$

Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:

$2(-1) + 3y = 4$

Solving for $y$, we get:

$y = 2$

Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:

$3(-1) + 5(2) = 7$

$10(-1) + 15(2) = 20$

Both equations are true, so our solution is correct.