what is the solution to this system of equations? 4x + 5y = 7 3x - 2y = -12 the solution is

Explanation:

Step1: Multiply equations to eliminate a variable

Multiply the first equation $4x + 5y=7$ by 2 and the second equation $3x - 2y=-12$ by 5. The first - multiplied equation: $2(4x + 5y)=2\times7$, which simplifies to $8x+10y = 14$. The second - multiplied equation: $5(3x - 2y)=5\times(-12)$, which simplifies to $15x-10y=-60$.

Step2: Add the two new - equations

$(8x + 10y)+(15x-10y)=14+( - 60)$. Combining like - terms, we get $8x+15x+10y - 10y=14 - 60$, so $23x=-46$. Solve for $x$: $x=\frac{-46}{23}=-2$.

Step3: Substitute $x$ into one of the original equations

Substitute $x = - 2$ into the first equation $4x + 5y=7$. We have $4\times(-2)+5y=7$. This simplifies to $-8 + 5y=7$. Add 8 to both sides: $5y=7 + 8=15$. Solve for $y$: $y=\frac{15}{5}=3$.

Answer:

$x=-2,y = 3$