Question

solve the system of linear equations by graphing. round the solution to the nearest tenth as needed.
y + 2.3 = 0.45x
-2y = 4.2x - 7.8
○ (2.4, -1.2)
○ (-1, 2.5)
○ no solution
○ infinitely many solutions

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(y + 2.3=0.45x\), we can rewrite it as \(y = 0.45x-2.3\). The slope \(m_1 = 0.45\) and the y - intercept \(b_1=- 2.3\).

For the second equation \(-2y = 4.2x-7.8\), divide both sides by \(- 2\):
\(y=\frac{4.2x - 7.8}{-2}=- 2.1x + 3.9\). The slope \(m_2=-2.1\) and the y - intercept \(b_2 = 3.9\).

Step2: Find the intersection point (solution)

We can also solve the system by substitution or elimination. Let's use substitution. Substitute \(y = 0.45x-2.3\) into \(-2y=4.2x - 7.8\):

\(-2(0.45x - 2.3)=4.2x-7.8\)

Expand the left - hand side: \(-0.9x + 4.6=4.2x-7.8\)

Add \(0.9x\) to both sides: \(4.6=4.2x + 0.9x-7.8\)

Combine like terms: \(4.6 = 5.1x-7.8\)

Add \(7.8\) to both sides: \(4.6 + 7.8=5.1x\)

\(12.4 = 5.1x\)

Solve for \(x\): \(x=\frac{12.4}{5.1}\approx2.4\)

Now substitute \(x = 2.4\) into \(y = 0.45x-2.3\):

\(y=0.45\times2.4-2.3=1.08 - 2.3=-1.22\approx - 1.2\)

Answer:

\((2.4,-1.2)\)