Question

Review the graphs of a system of these two linear equations in two vanables y = 4z-10 and y=-2x+8 Find the solution of the system.

(1 point)

The solution of the system of equations is (

Answer 1

To find the solution of the system of equations given by \( y = 4z - 10 \) and \( y = -2x + 8 \), we first need to find the point where the two lines intersect, which represents the solution to the system.

Since the equations are in terms of \( y \), we can set them equal to each other:

\[
4z - 10 = -2x + 8
\]

To express \( z \) in terms of \( x \), we rearrange the equation:

1. Add 10 to both sides:
\[
4z = -2x + 18
\]

2. Divide by 4:
\[
z = -\frac{1}{2}x + \frac{9}{2}
\]

Now we can express \( y \) in terms of \( x \) as well by substituting different values of \( x \):

To find a specific solution, we can solve for both equations.

From equation \( y = -2x + 8 \), we can input various \( x \) values to find corresponding \( y \) values, or vice versa.

However, to find a specific intersection, we would typically solve for \( x \) and then determine \( y \):
For example, if we want to set \( z = 0 \) to find \( x \):

From \( z=0 \):
\[
y = -\frac{1}{2}(0) + \frac{9}{2} = \frac{9}{2} = 4.5
\]
And from \( y = -2x + 8 \):
\[
4.5 = -2x + 8 \implies -2x = 4.5 - 8 \implies -2x = -3.5 \implies x = 1.75
\]

Now substituting \( x = 1.75 \) into one of the equations for \( z \):
\[
z = -\frac{1}{2}(1.75) + \frac{9}{2} \implies z = -0.875 + 4.5 \implies z = 3.625
\]

The solution of the system can be expressed as \( (x, y, z) = (1.75, 4.5, 3.625) \).

Thus, the point of intersection or solution of the system of equations can be summarized in a more standard form as:
\[
\text{(x, y) intersection point: } (1.75, 4.5)
\] since we have not defined "z" in the original equations explicitly when solving.

So, in answer to your question, the solution of the system of equations is:
\((1.75, 4.5)\) if only considering the x and y intersections.