Question

11. What is the value of xin the solution to this system of equations?

3x - 5y = 22
y = -5x + 32

Answer 1

x = ¹³⁄₂

y = ⁻¹⁄₂

Step-by-step explanation:

`\bold{\begin{bmatrix}3x-5y=22\\ y=-5x+32\end{bmatrix}}`

• Substitute y = -5x + 32

`\bold{\begin{bmatrix}3x-5\left(-5x+32\right)=22\end{bmatrix}}`

• Simplify

`\bold{\begin{bmatrix}28x-160=22\end{bmatrix}}`

• Isolate x for 28x - 160 - 22: x = ¹³⁄₂

`\bold{\mathrm{For\:}y=-5x+32}`

• Substitute x = ¹³⁄₂

`\bold{y=-5\cdot (13)/(2)+32}`

-5 · ¹³⁄₂ + 32 = ⁻¹⁄₂

• y = ⁻¹⁄₂

x = ¹³⁄₂

y = ⁻¹⁄₂

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