Solve the system of equations 5, x, plus, 8, y, equals, minus, 145x+8y=−14 and minus, 3, x, minus, 2, y, equals, 0−3x−2y=0 by combining the equations.

Question

Solve the system of equations 5, x, plus, 8, y, equals, minus, 145x+8y=−14 and minus, 3, x, minus, 2, y, equals, 0−3x−2y=0 by combining the equations.
Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, 5, x(5x	plus, 8, y+8y	equals=	minus, 14, right parenthesis−14)
left parenthesis, minus, 3, x(−3x	minus, 2, y−2y	equals=	0, right parenthesis0)
5, x5x	plus, 8, y+8y	equals=	minus, 14−14
minus, 3, x−3x	minus, 2, y−2y	equals=	00
0
0xx	plus+
0
0yy	equals=

GPT-4o mini · Answer

To solve the system of equations 1. $ 5x + 8y = -14 $ 2. $ -3x - 2y = 0 $ we will use the method of elimination (combining the equations). To make the calculations easier, we will first express one equation in a form that allows us to eliminate one variable. **Step 1: Rearranging the second equation to express $y$:** From the second equation, we can express $y$ in terms of $x$: $$ -3x - 2y = 0 \implies 2y = -3x \implies y = -\frac{3}{2}x $$ **Step 2: Substitute $y$ into the first equation:** Now that we have $y$ in terms of $x$, we can substitute it into the first equation: $$ 5x + 8\left(-\frac{3}{2}x\right) = -14 $$ **Step 3: Simplifying the equation:** $$ 5x - 12x = -14 $$ $$ -7x = -14 $$ **Step 4: Solve for $x$:** $$ x = \frac{-14}{-7} = 2 $$ **Step 5: Substitute $x$ back to find $y$:** Now substitute $x = 2$ back into the equation for $y$: $$ y = -\frac{3}{2}(2) = -3 $$ **Final Solution:** The solutions to the system of equations are: $$ x = 2, \quad y = -3 $$ Thus, the ordered pair that solves the system is $(2, -3)$.