Answer:
To solve the system of equations and write each equation in slope-intercept form, we can follow these steps:
1. Equation 1: 2x + y = 3
To write this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.
First, subtract 2x from both sides of the equation:
y = -2x + 3
Now the equation is in slope-intercept form.
2. Equation 2: -2y = 14 - 6x
To write this equation in slope-intercept form, we need to isolate y.
First, divide both sides of the equation by -2 to solve for y:
y = (-14 + 6x) / 2
y = -7 + 3x
Now the equation is in slope-intercept form.
To solve the system of equations, we can set the two equations equal to each other and solve for x:
-2x + 3 = -7 + 3x
Add 2x to both sides:
3 = 5x - 7
Add 7 to both sides:
10 = 5x
Divide both sides by 5:
x = 2
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use Equation 1:
2(2) + y = 3
4 + y = 3
y = -1
Therefore, the solution to the system of equations is x = 2 and y = -1. The equations in slope-intercept form are:
Equation 1: y = -2x + 3
Equation 2: y = -7 + 3x
Explanation: