1/2x-3/4y=-3-1/2; find value of x
2x-3=x-3y-1; find valud of y
1. graph
2. solve by substitution
To find the value of x in the equation 1/2x - 3/4y = -3 - 1/2, we can use either the graphing method or the substitution method.
1. Graphing Method:
To solve the equation graphically, we can rearrange it to the standard form of a linear equation: Ax + By = C.
In this case, the equation becomes 1/2x - 3/4y = -3 - 1/2 can be rewritten as:
2(1/2x) - 4(3/4y) = 2(-3 - 1/2).
Simplifying this equation gives us:
x - 3y = -6.
Now we can graph the linear equation x - 3y = -6 on a graphing plane. The x-intercept (where the line crosses the x-axis) and the y-intercept (where the line crosses the y-axis) can be found by setting either x or y to zero.
When setting x = 0, we have:
0 - 3y = -6.
Solving for y, we find y = 2.
When setting y = 0, we have:
x - 0 = -6.
Solving for x, we find x = -6.
Plot these two points (0, 2) and (-6, 0) on the graphing plane and draw a straight line passing through these points. The value of x can be determined by reading the x-coordinate where the line intersects the x-axis.
2. Substitution Method:
To solve the equation 1/2x - 3/4y = -3 - 1/2 using the substitution method, we can isolate one variable (x or y) in terms of the other variable, then substitute it into the other equation.
Given: 1/2x - 3/4y = -3 - 1/2.
Let's solve this equation to find x:
1/2x - 3/4y = -3 - 1/2.
Multiply all terms by the least common denominator, which is 4:
4(1/2x) - 4(3/4y) = 4(-3 - 1/2).
Simplifying further, we get:
2x - 3y = -12.
Now, we have a new equation: 2x - 3y = -12.
To find the value of x, we need another equation from the given information.
Please provide the second equation to proceed with solving for x and y.